task_id stringlengths 23 52 | subset stringclasses 1
value | family stringclasses 80
values | problem_key stringclasses 75
values | domain stringclasses 8
values | tier stringclasses 2
values | level stringclasses 6
values | source stringclasses 80
values | license stringclasses 3
values | tags listlengths 0 4 | prompt stringlengths 308 37k | instance stringlengths 56 37.8k | direction null | baseline null | best_known null | reference_answer stringlengths 8 198k | reference_reward float64 1 1 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
construct-rlve-min-chromatic-number-l4-s6 | construct | rlve_min_chromatic_number | graph_k_coloring_chromatic | graph_theory | competition | 4 | RLVE-Gym/minimum_chromatic_number | MIT | [
"agentic_trivial",
"np_search"
] | An undirected simple graph has 18 vertices labelled 0..17 and edge list
[[0, 2], [0, 3], [0, 4], [0, 7], [0, 10], [0, 11], [0, 12], [0, 13], [0, 14], [0, 15], [0, 16], [0, 17], [1, 2], [1, 3], [1, 5], [1, 6], [1, 8], [1, 9], [1, 10], [1, 12], [1, 14], [1, 15], [1, 16], [1, 17], [2, 3], [2, 4], [2, 5], [2, 7], [2, 8], [... | {"n": 18, "k": 7, "edges": [[0, 2], [0, 3], [0, 4], [0, 7], [0, 10], [0, 11], [0, 12], [0, 13], [0, 14], [0, 15], [0, 16], [0, 17], [1, 2], [1, 3], [1, 5], [1, 6], [1, 8], [1, 9], [1, 10], [1, 12], [1, 14], [1, 15], [1, 16], [1, 17], [2, 3], [2, 4], [2, 5], [2, 7], [2, 8], [2, 10], [2, 11], [2, 13], [2, 14], [2, 15], [... | null | null | null | {"colors": [0, 0, 1, 2, 3, 4, 1, 4, 5, 1, 5, 4, 6, 3, 3, 5, 6, 2]} | 1 |
construct-rlve-min-chromatic-number-l4-s7 | construct | rlve_min_chromatic_number | graph_k_coloring_chromatic | graph_theory | competition | 4 | RLVE-Gym/minimum_chromatic_number | MIT | [
"agentic_trivial",
"np_search"
] | An undirected simple graph has 18 vertices labelled 0..17 and edge list
[[0, 2], [0, 4], [0, 11], [0, 13], [0, 14], [0, 15], [0, 16], [1, 4], [1, 6], [1, 7], [1, 17], [2, 5], [2, 13], [3, 9], [3, 16], [3, 17], [4, 9], [4, 10], [4, 16], [5, 10], [5, 11], [5, 12], [5, 13], [5, 15], [5, 16], [6, 8], [6, 12], [6, 14], [6, ... | {"n": 18, "k": 4, "edges": [[0, 2], [0, 4], [0, 11], [0, 13], [0, 14], [0, 15], [0, 16], [1, 4], [1, 6], [1, 7], [1, 17], [2, 5], [2, 13], [3, 9], [3, 16], [3, 17], [4, 9], [4, 10], [4, 16], [5, 10], [5, 11], [5, 12], [5, 13], [5, 15], [5, 16], [6, 8], [6, 12], [6, 14], [6, 17], [7, 17], [8, 16], [8, 17], [9, 10], [9, ... | null | null | null | {"colors": [0, 0, 1, 0, 1, 0, 2, 2, 0, 2, 3, 2, 1, 2, 1, 2, 2, 1]} | 1 |
construct-rlve-min-chromatic-number-l4-s8 | construct | rlve_min_chromatic_number | graph_k_coloring_chromatic | graph_theory | competition | 4 | RLVE-Gym/minimum_chromatic_number | MIT | [
"agentic_trivial",
"np_search"
] | An undirected simple graph has 18 vertices labelled 0..17 and edge list
[[0, 1], [0, 8], [0, 11], [0, 16], [0, 17], [1, 5], [1, 8], [1, 11], [1, 13], [1, 14], [1, 15], [1, 16], [2, 3], [2, 8], [2, 9], [2, 12], [2, 13], [2, 15], [2, 17], [3, 7], [3, 8], [3, 9], [3, 10], [3, 12], [3, 13], [3, 17], [4, 6], [4, 7], [4, 10]... | {"n": 18, "k": 5, "edges": [[0, 1], [0, 8], [0, 11], [0, 16], [0, 17], [1, 5], [1, 8], [1, 11], [1, 13], [1, 14], [1, 15], [1, 16], [2, 3], [2, 8], [2, 9], [2, 12], [2, 13], [2, 15], [2, 17], [3, 7], [3, 8], [3, 9], [3, 10], [3, 12], [3, 13], [3, 17], [4, 6], [4, 7], [4, 10], [4, 11], [4, 13], [4, 14], [4, 16], [4, 17]... | null | null | null | {"colors": [0, 1, 0, 1, 1, 0, 2, 3, 3, 2, 0, 2, 4, 2, 0, 4, 3, 4]} | 1 |
construct-rlve-min-chromatic-number-l4-s9 | construct | rlve_min_chromatic_number | graph_k_coloring_chromatic | graph_theory | competition | 4 | RLVE-Gym/minimum_chromatic_number | MIT | [
"agentic_trivial",
"np_search"
] | An undirected simple graph has 18 vertices labelled 0..17 and edge list
[[0, 1], [0, 2], [0, 5], [0, 8], [0, 9], [0, 10], [0, 11], [0, 12], [0, 13], [0, 15], [0, 16], [0, 17], [1, 3], [1, 4], [1, 6], [1, 7], [1, 8], [1, 9], [1, 11], [1, 12], [1, 13], [1, 14], [1, 15], [1, 16], [1, 17], [2, 3], [2, 4], [2, 5], [2, 6], [... | {"n": 18, "k": 7, "edges": [[0, 1], [0, 2], [0, 5], [0, 8], [0, 9], [0, 10], [0, 11], [0, 12], [0, 13], [0, 15], [0, 16], [0, 17], [1, 3], [1, 4], [1, 6], [1, 7], [1, 8], [1, 9], [1, 11], [1, 12], [1, 13], [1, 14], [1, 15], [1, 16], [1, 17], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], [2, 8], [2, 13], [2, 14], [2, 15], [2,... | null | null | null | {"colors": [0, 1, 1, 2, 0, 2, 0, 3, 4, 3, 1, 5, 4, 5, 6, 4, 2, 6]} | 1 |
construct-rlve-min-chromatic-number-l5-s0 | construct | rlve_min_chromatic_number | graph_k_coloring_chromatic | graph_theory | competition | 5 | RLVE-Gym/minimum_chromatic_number | MIT | [
"agentic_trivial",
"np_search"
] | An undirected simple graph has 24 vertices labelled 0..23 and edge list
[[0, 2], [0, 6], [0, 9], [0, 10], [0, 11], [0, 12], [0, 13], [0, 16], [0, 17], [0, 20], [1, 4], [1, 6], [1, 8], [1, 14], [1, 17], [1, 19], [1, 20], [1, 21], [1, 23], [2, 3], [2, 5], [2, 9], [2, 10], [2, 13], [2, 19], [2, 20], [2, 22], [3, 4], [3, 7... | {"n": 24, "k": 6, "edges": [[0, 2], [0, 6], [0, 9], [0, 10], [0, 11], [0, 12], [0, 13], [0, 16], [0, 17], [0, 20], [1, 4], [1, 6], [1, 8], [1, 14], [1, 17], [1, 19], [1, 20], [1, 21], [1, 23], [2, 3], [2, 5], [2, 9], [2, 10], [2, 13], [2, 19], [2, 20], [2, 22], [3, 4], [3, 7], [3, 10], [3, 11], [3, 14], [3, 15], [3, 16... | null | null | null | {"colors": [0, 1, 1, 0, 2, 2, 3, 4, 3, 5, 3, 1, 1, 2, 4, 5, 3, 5, 1, 2, 4, 0, 0, 2]} | 1 |
construct-rlve-min-chromatic-number-l5-s1 | construct | rlve_min_chromatic_number | graph_k_coloring_chromatic | graph_theory | competition | 5 | RLVE-Gym/minimum_chromatic_number | MIT | [
"agentic_trivial",
"np_search"
] | An undirected simple graph has 24 vertices labelled 0..23 and edge list
[[0, 4], [0, 7], [0, 9], [0, 10], [0, 11], [0, 14], [0, 18], [0, 19], [0, 21], [1, 5], [1, 6], [1, 9], [1, 11], [1, 12], [1, 13], [1, 15], [1, 16], [1, 17], [1, 18], [1, 19], [1, 22], [2, 3], [2, 4], [2, 9], [2, 12], [2, 13], [2, 15], [2, 16], [2, ... | {"n": 24, "k": 6, "edges": [[0, 4], [0, 7], [0, 9], [0, 10], [0, 11], [0, 14], [0, 18], [0, 19], [0, 21], [1, 5], [1, 6], [1, 9], [1, 11], [1, 12], [1, 13], [1, 15], [1, 16], [1, 17], [1, 18], [1, 19], [1, 22], [2, 3], [2, 4], [2, 9], [2, 12], [2, 13], [2, 15], [2, 16], [2, 18], [2, 19], [2, 21], [3, 4], [3, 10], [3, 1... | null | null | null | {"colors": [0, 0, 0, 1, 2, 3, 1, 3, 0, 1, 3, 4, 2, 1, 2, 5, 5, 4, 5, 1, 5, 4, 2, 0]} | 1 |
construct-rlve-min-chromatic-number-l5-s2 | construct | rlve_min_chromatic_number | graph_k_coloring_chromatic | graph_theory | competition | 5 | RLVE-Gym/minimum_chromatic_number | MIT | [
"agentic_trivial",
"np_search"
] | An undirected simple graph has 24 vertices labelled 0..23 and edge list
[[0, 2], [0, 3], [0, 4], [0, 5], [0, 7], [0, 9], [0, 10], [0, 11], [0, 13], [0, 14], [0, 16], [0, 17], [0, 18], [0, 19], [0, 20], [0, 21], [0, 22], [0, 23], [1, 3], [1, 5], [1, 6], [1, 7], [1, 10], [1, 11], [1, 13], [1, 14], [1, 17], [1, 19], [1, 2... | {"n": 24, "k": 8, "edges": [[0, 2], [0, 3], [0, 4], [0, 5], [0, 7], [0, 9], [0, 10], [0, 11], [0, 13], [0, 14], [0, 16], [0, 17], [0, 18], [0, 19], [0, 20], [0, 21], [0, 22], [0, 23], [1, 3], [1, 5], [1, 6], [1, 7], [1, 10], [1, 11], [1, 13], [1, 14], [1, 17], [1, 19], [1, 20], [1, 21], [1, 22], [1, 23], [2, 4], [2, 5]... | null | null | null | {"colors": [0, 0, 1, 1, 2, 2, 3, 3, 0, 2, 4, 5, 2, 3, 5, 4, 6, 7, 4, 6, 7, 6, 5, 1]} | 1 |
construct-rlve-min-chromatic-number-l5-s3 | construct | rlve_min_chromatic_number | graph_k_coloring_chromatic | graph_theory | competition | 5 | RLVE-Gym/minimum_chromatic_number | MIT | [
"agentic_trivial",
"np_search"
] | An undirected simple graph has 24 vertices labelled 0..23 and edge list
[[0, 1], [0, 7], [0, 8], [0, 10], [0, 14], [0, 16], [0, 20], [0, 21], [0, 22], [0, 23], [1, 3], [1, 5], [1, 9], [1, 10], [1, 13], [1, 14], [1, 15], [1, 22], [2, 4], [2, 5], [2, 9], [2, 10], [2, 14], [2, 17], [2, 18], [2, 21], [3, 9], [3, 10], [3, 1... | {"n": 24, "k": 6, "edges": [[0, 1], [0, 7], [0, 8], [0, 10], [0, 14], [0, 16], [0, 20], [0, 21], [0, 22], [0, 23], [1, 3], [1, 5], [1, 9], [1, 10], [1, 13], [1, 14], [1, 15], [1, 22], [2, 4], [2, 5], [2, 9], [2, 10], [2, 14], [2, 17], [2, 18], [2, 21], [3, 9], [3, 10], [3, 11], [3, 12], [3, 13], [3, 16], [3, 17], [3, 2... | null | null | null | {"colors": [0, 1, 0, 0, 1, 2, 0, 3, 4, 5, 2, 5, 3, 5, 4, 0, 3, 1, 3, 1, 1, 2, 2, 4]} | 1 |
construct-rlve-min-chromatic-number-l5-s4 | construct | rlve_min_chromatic_number | graph_k_coloring_chromatic | graph_theory | competition | 5 | RLVE-Gym/minimum_chromatic_number | MIT | [
"agentic_trivial",
"np_search"
] | An undirected simple graph has 24 vertices labelled 0..23 and edge list
[[0, 5], [0, 6], [0, 8], [0, 9], [0, 10], [0, 11], [0, 14], [0, 16], [0, 17], [0, 20], [1, 2], [1, 3], [1, 9], [1, 10], [1, 11], [1, 14], [1, 16], [1, 19], [1, 21], [1, 22], [2, 6], [2, 7], [2, 8], [2, 9], [2, 10], [2, 13], [2, 14], [2, 16], [2, 17... | {"n": 24, "k": 7, "edges": [[0, 5], [0, 6], [0, 8], [0, 9], [0, 10], [0, 11], [0, 14], [0, 16], [0, 17], [0, 20], [1, 2], [1, 3], [1, 9], [1, 10], [1, 11], [1, 14], [1, 16], [1, 19], [1, 21], [1, 22], [2, 6], [2, 7], [2, 8], [2, 9], [2, 10], [2, 13], [2, 14], [2, 16], [2, 17], [2, 18], [2, 22], [3, 4], [3, 5], [3, 6], ... | null | null | null | {"colors": [0, 0, 1, 1, 2, 3, 2, 0, 4, 5, 4, 3, 1, 6, 4, 1, 6, 6, 0, 2, 6, 5, 5, 3]} | 1 |
construct-rlve-min-chromatic-number-l5-s5 | construct | rlve_min_chromatic_number | graph_k_coloring_chromatic | graph_theory | competition | 5 | RLVE-Gym/minimum_chromatic_number | MIT | [
"agentic_trivial",
"np_search"
] | An undirected simple graph has 24 vertices labelled 0..23 and edge list
[[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 10], [0, 11], [0, 12], [0, 15], [0, 16], [0, 17], [0, 18], [0, 19], [0, 20], [0, 21], [0, 22], [1, 2], [1, 4], [1, 9], [1, 10], [1, 11], [1, 12], [1, 13], [1, 14], [1, 15], [1, 16... | {"n": 24, "k": 9, "edges": [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 10], [0, 11], [0, 12], [0, 15], [0, 16], [0, 17], [0, 18], [0, 19], [0, 20], [0, 21], [0, 22], [1, 2], [1, 4], [1, 9], [1, 10], [1, 11], [1, 12], [1, 13], [1, 14], [1, 15], [1, 16], [1, 17], [1, 18], [1, 19], [1, 21], [1, 22... | null | null | null | {"colors": [0, 1, 2, 1, 3, 4, 5, 6, 4, 0, 5, 2, 4, 0, 2, 7, 8, 8, 3, 7, 7, 5, 6, 1]} | 1 |
construct-rlve-min-chromatic-number-l5-s6 | construct | rlve_min_chromatic_number | graph_k_coloring_chromatic | graph_theory | competition | 5 | RLVE-Gym/minimum_chromatic_number | MIT | [
"agentic_trivial",
"np_search"
] | An undirected simple graph has 24 vertices labelled 0..23 and edge list
[[0, 1], [0, 4], [0, 5], [0, 6], [0, 7], [0, 11], [0, 12], [0, 14], [0, 18], [0, 19], [0, 20], [0, 22], [1, 2], [1, 5], [1, 9], [1, 15], [1, 22], [1, 23], [2, 5], [2, 7], [2, 14], [2, 17], [2, 20], [2, 21], [2, 22], [2, 23], [3, 4], [3, 6], [3, 7],... | {"n": 24, "k": 5, "edges": [[0, 1], [0, 4], [0, 5], [0, 6], [0, 7], [0, 11], [0, 12], [0, 14], [0, 18], [0, 19], [0, 20], [0, 22], [1, 2], [1, 5], [1, 9], [1, 15], [1, 22], [1, 23], [2, 5], [2, 7], [2, 14], [2, 17], [2, 20], [2, 21], [2, 22], [2, 23], [3, 4], [3, 6], [3, 7], [3, 8], [3, 10], [3, 11], [3, 17], [3, 21], ... | null | null | null | {"colors": [0, 1, 0, 0, 1, 2, 1, 2, 1, 0, 1, 1, 2, 0, 3, 3, 4, 4, 4, 1, 4, 3, 3, 2]} | 1 |
construct-rlve-min-chromatic-number-l5-s7 | construct | rlve_min_chromatic_number | graph_k_coloring_chromatic | graph_theory | competition | 5 | RLVE-Gym/minimum_chromatic_number | MIT | [
"agentic_trivial",
"np_search"
] | An undirected simple graph has 24 vertices labelled 0..23 and edge list
[[0, 8], [0, 11], [0, 12], [0, 14], [0, 17], [0, 18], [0, 19], [0, 22], [1, 7], [1, 9], [1, 10], [1, 15], [1, 18], [1, 20], [1, 21], [1, 23], [2, 3], [2, 5], [2, 7], [2, 9], [2, 11], [2, 12], [2, 14], [2, 23], [3, 7], [3, 9], [3, 10], [3, 13], [3, ... | {"n": 24, "k": 4, "edges": [[0, 8], [0, 11], [0, 12], [0, 14], [0, 17], [0, 18], [0, 19], [0, 22], [1, 7], [1, 9], [1, 10], [1, 15], [1, 18], [1, 20], [1, 21], [1, 23], [2, 3], [2, 5], [2, 7], [2, 9], [2, 11], [2, 12], [2, 14], [2, 23], [3, 7], [3, 9], [3, 10], [3, 13], [3, 22], [4, 6], [4, 9], [4, 14], [4, 19], [4, 20... | null | null | null | {"colors": [0, 1, 1, 0, 1, 0, 0, 2, 1, 3, 2, 3, 3, 2, 2, 0, 1, 1, 2, 3, 0, 3, 1, 0]} | 1 |
construct-rlve-min-chromatic-number-l5-s8 | construct | rlve_min_chromatic_number | graph_k_coloring_chromatic | graph_theory | competition | 5 | RLVE-Gym/minimum_chromatic_number | MIT | [
"agentic_trivial",
"np_search"
] | An undirected simple graph has 24 vertices labelled 0..23 and edge list
[[0, 3], [0, 4], [0, 5], [0, 7], [0, 10], [0, 12], [0, 14], [0, 17], [0, 18], [0, 19], [1, 6], [1, 7], [1, 13], [1, 19], [1, 20], [1, 21], [2, 3], [2, 4], [2, 6], [2, 13], [2, 21], [3, 8], [3, 10], [3, 11], [3, 15], [3, 16], [3, 18], [3, 21], [3, 2... | {"n": 24, "k": 5, "edges": [[0, 3], [0, 4], [0, 5], [0, 7], [0, 10], [0, 12], [0, 14], [0, 17], [0, 18], [0, 19], [1, 6], [1, 7], [1, 13], [1, 19], [1, 20], [1, 21], [2, 3], [2, 4], [2, 6], [2, 13], [2, 21], [3, 8], [3, 10], [3, 11], [3, 15], [3, 16], [3, 18], [3, 21], [3, 23], [4, 5], [4, 6], [4, 8], [4, 11], [4, 15],... | null | null | null | {"colors": [0, 0, 0, 1, 1, 2, 2, 1, 0, 3, 2, 0, 2, 1, 1, 2, 3, 3, 4, 1, 4, 3, 0, 3]} | 1 |
construct-rlve-min-chromatic-number-l5-s9 | construct | rlve_min_chromatic_number | graph_k_coloring_chromatic | graph_theory | competition | 5 | RLVE-Gym/minimum_chromatic_number | MIT | [
"agentic_trivial",
"np_search"
] | An undirected simple graph has 24 vertices labelled 0..23 and edge list
[[0, 2], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 11], [0, 12], [0, 14], [0, 15], [0, 18], [0, 20], [0, 22], [1, 3], [1, 4], [1, 7], [1, 10], [1, 11], [1, 15], [1, 17], [1, 18], [1, 20], [2, 3], [2, 7], [2, 8], [2, 9], [2, 10], [2, 11], [2, 17],... | {"n": 24, "k": 6, "edges": [[0, 2], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 11], [0, 12], [0, 14], [0, 15], [0, 18], [0, 20], [0, 22], [1, 3], [1, 4], [1, 7], [1, 10], [1, 11], [1, 15], [1, 17], [1, 18], [1, 20], [2, 3], [2, 7], [2, 8], [2, 9], [2, 10], [2, 11], [2, 17], [2, 18], [2, 19], [2, 21], [3, 6], [3, 8], [... | null | null | null | {"colors": [0, 0, 1, 2, 1, 1, 3, 2, 4, 3, 5, 5, 4, 3, 4, 4, 3, 4, 3, 0, 5, 2, 5, 0]} | 1 |
construct-rlve-min-chromatic-number-l6-s0 | construct | rlve_min_chromatic_number | graph_k_coloring_chromatic | graph_theory | competition | 6 | RLVE-Gym/minimum_chromatic_number | MIT | [
"agentic_trivial",
"np_search"
] | An undirected simple graph has 30 vertices labelled 0..29 and edge list
[[0, 7], [0, 9], [0, 12], [0, 13], [0, 14], [0, 16], [0, 24], [0, 25], [1, 5], [1, 6], [1, 10], [1, 12], [1, 15], [1, 19], [1, 24], [1, 28], [2, 10], [2, 11], [2, 12], [2, 21], [2, 27], [3, 15], [4, 11], [4, 12], [4, 19], [4, 24], [4, 28], [4, 29],... | {"n": 30, "k": 5, "edges": [[0, 7], [0, 9], [0, 12], [0, 13], [0, 14], [0, 16], [0, 24], [0, 25], [1, 5], [1, 6], [1, 10], [1, 12], [1, 15], [1, 19], [1, 24], [1, 28], [2, 10], [2, 11], [2, 12], [2, 21], [2, 27], [3, 15], [4, 11], [4, 12], [4, 19], [4, 24], [4, 28], [4, 29], [5, 9], [5, 10], [5, 15], [5, 18], [5, 26], ... | null | null | null | {"colors": [0, 0, 0, 0, 0, 1, 1, 2, 0, 3, 2, 2, 1, 2, 4, 4, 3, 0, 0, 2, 1, 3, 0, 3, 4, 1, 0, 3, 4, 2]} | 1 |
construct-rlve-min-chromatic-number-l6-s1 | construct | rlve_min_chromatic_number | graph_k_coloring_chromatic | graph_theory | competition | 6 | RLVE-Gym/minimum_chromatic_number | MIT | [
"agentic_trivial",
"np_search"
] | An undirected simple graph has 30 vertices labelled 0..29 and edge list
[[0, 2], [0, 6], [0, 8], [0, 11], [0, 14], [0, 16], [0, 18], [0, 28], [1, 9], [1, 10], [1, 14], [1, 15], [1, 16], [1, 17], [1, 19], [1, 22], [1, 25], [1, 26], [1, 29], [2, 8], [2, 9], [2, 13], [2, 14], [2, 20], [2, 27], [3, 5], [3, 13], [3, 21], [3... | {"n": 30, "k": 4, "edges": [[0, 2], [0, 6], [0, 8], [0, 11], [0, 14], [0, 16], [0, 18], [0, 28], [1, 9], [1, 10], [1, 14], [1, 15], [1, 16], [1, 17], [1, 19], [1, 22], [1, 25], [1, 26], [1, 29], [2, 8], [2, 9], [2, 13], [2, 14], [2, 20], [2, 27], [3, 5], [3, 13], [3, 21], [3, 22], [3, 29], [4, 6], [4, 9], [4, 13], [4, ... | null | null | null | {"colors": [0, 1, 1, 1, 1, 2, 3, 2, 2, 0, 0, 1, 1, 0, 2, 2, 3, 2, 1, 0, 0, 3, 3, 1, 0, 3, 2, 0, 3, 2]} | 1 |
construct-rlve-min-chromatic-number-l6-s2 | construct | rlve_min_chromatic_number | graph_k_coloring_chromatic | graph_theory | competition | 6 | RLVE-Gym/minimum_chromatic_number | MIT | [
"agentic_trivial",
"np_search"
] | An undirected simple graph has 30 vertices labelled 0..29 and edge list
[[0, 1], [0, 2], [0, 5], [0, 6], [0, 8], [0, 10], [0, 11], [0, 12], [0, 14], [0, 15], [0, 16], [0, 17], [0, 18], [0, 20], [0, 21], [0, 22], [0, 23], [0, 24], [0, 25], [0, 26], [0, 27], [0, 28], [1, 2], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9]... | {"n": 30, "k": 11, "edges": [[0, 1], [0, 2], [0, 5], [0, 6], [0, 8], [0, 10], [0, 11], [0, 12], [0, 14], [0, 15], [0, 16], [0, 17], [0, 18], [0, 20], [0, 21], [0, 22], [0, 23], [0, 24], [0, 25], [0, 26], [0, 27], [0, 28], [1, 2], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [1, 10], [1, 11], [1, 12], [1, 13], [1, 16... | null | null | null | {"colors": [0, 1, 2, 1, 2, 3, 3, 0, 4, 0, 5, 6, 7, 0, 5, 1, 8, 4, 6, 4, 9, 10, 6, 7, 3, 10, 5, 7, 8, 9]} | 1 |
construct-rlve-min-chromatic-number-l6-s3 | construct | rlve_min_chromatic_number | graph_k_coloring_chromatic | graph_theory | competition | 6 | RLVE-Gym/minimum_chromatic_number | MIT | [
"agentic_trivial",
"np_search"
] | An undirected simple graph has 30 vertices labelled 0..29 and edge list
[[0, 1], [0, 4], [0, 9], [0, 18], [0, 21], [0, 26], [1, 3], [1, 6], [1, 7], [1, 13], [1, 21], [1, 27], [2, 10], [2, 11], [2, 14], [2, 19], [2, 21], [2, 22], [3, 5], [3, 6], [3, 15], [3, 16], [3, 18], [3, 20], [3, 29], [4, 7], [4, 13], [4, 18], [4, ... | {"n": 30, "k": 4, "edges": [[0, 1], [0, 4], [0, 9], [0, 18], [0, 21], [0, 26], [1, 3], [1, 6], [1, 7], [1, 13], [1, 21], [1, 27], [2, 10], [2, 11], [2, 14], [2, 19], [2, 21], [2, 22], [3, 5], [3, 6], [3, 15], [3, 16], [3, 18], [3, 20], [3, 29], [4, 7], [4, 13], [4, 18], [4, 19], [4, 20], [4, 21], [4, 25], [5, 9], [5, 1... | null | null | null | {"colors": [0, 1, 0, 0, 1, 2, 2, 0, 0, 1, 1, 2, 1, 0, 1, 3, 3, 0, 3, 3, 2, 3, 2, 0, 1, 0, 1, 0, 2, 1]} | 1 |
construct-rlve-min-chromatic-number-l6-s4 | construct | rlve_min_chromatic_number | graph_k_coloring_chromatic | graph_theory | competition | 6 | RLVE-Gym/minimum_chromatic_number | MIT | [
"agentic_trivial",
"np_search"
] | An undirected simple graph has 30 vertices labelled 0..29 and edge list
[[0, 1], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [0, 10], [0, 11], [0, 12], [0, 13], [0, 14], [0, 15], [0, 16], [0, 20], [0, 21], [0, 22], [0, 23], [0, 24], [0, 25], [0, 26], [0, 28], [1, 2], [1, 3], [1, 4], [1, 6], [1, 7], [1, 8], ... | {"n": 30, "k": 11, "edges": [[0, 1], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [0, 10], [0, 11], [0, 12], [0, 13], [0, 14], [0, 15], [0, 16], [0, 20], [0, 21], [0, 22], [0, 23], [0, 24], [0, 25], [0, 26], [0, 28], [1, 2], [1, 3], [1, 4], [1, 6], [1, 7], [1, 8], [1, 9], [1, 10], [1, 11], [1, 13], [1, 15], ... | null | null | null | {"colors": [0, 1, 0, 2, 3, 1, 4, 2, 5, 6, 7, 6, 8, 4, 3, 7, 7, 1, 0, 9, 9, 5, 6, 10, 10, 8, 3, 2, 9, 5]} | 1 |
construct-rlve-min-chromatic-number-l6-s5 | construct | rlve_min_chromatic_number | graph_k_coloring_chromatic | graph_theory | competition | 6 | RLVE-Gym/minimum_chromatic_number | MIT | [
"agentic_trivial",
"np_search"
] | An undirected simple graph has 30 vertices labelled 0..29 and edge list
[[0, 1], [0, 2], [0, 4], [0, 8], [0, 9], [0, 13], [0, 18], [0, 19], [0, 22], [0, 28], [1, 2], [1, 6], [1, 7], [1, 9], [1, 15], [1, 21], [1, 23], [1, 27], [2, 7], [2, 10], [2, 12], [2, 23], [2, 24], [3, 14], [3, 16], [3, 19], [3, 23], [3, 25], [4, 7... | {"n": 30, "k": 4, "edges": [[0, 1], [0, 2], [0, 4], [0, 8], [0, 9], [0, 13], [0, 18], [0, 19], [0, 22], [0, 28], [1, 2], [1, 6], [1, 7], [1, 9], [1, 15], [1, 21], [1, 23], [1, 27], [2, 7], [2, 10], [2, 12], [2, 23], [2, 24], [3, 14], [3, 16], [3, 19], [3, 23], [3, 25], [4, 7], [4, 8], [4, 10], [4, 15], [4, 23], [4, 28]... | null | null | null | {"colors": [0, 1, 2, 2, 1, 1, 2, 3, 2, 2, 3, 0, 3, 2, 1, 2, 1, 1, 3, 3, 3, 0, 1, 0, 1, 3, 0, 0, 2, 2]} | 1 |
construct-rlve-min-chromatic-number-l6-s6 | construct | rlve_min_chromatic_number | graph_k_coloring_chromatic | graph_theory | competition | 6 | RLVE-Gym/minimum_chromatic_number | MIT | [
"agentic_trivial",
"np_search"
] | An undirected simple graph has 30 vertices labelled 0..29 and edge list
[[0, 1], [0, 13], [0, 19], [0, 20], [0, 21], [0, 22], [0, 24], [0, 26], [0, 27], [0, 28], [0, 29], [1, 2], [1, 3], [1, 7], [1, 9], [1, 11], [1, 12], [1, 14], [1, 15], [1, 20], [1, 21], [1, 24], [1, 26], [1, 28], [2, 3], [2, 7], [2, 8], [2, 10], [2,... | {"n": 30, "k": 6, "edges": [[0, 1], [0, 13], [0, 19], [0, 20], [0, 21], [0, 22], [0, 24], [0, 26], [0, 27], [0, 28], [0, 29], [1, 2], [1, 3], [1, 7], [1, 9], [1, 11], [1, 12], [1, 14], [1, 15], [1, 20], [1, 21], [1, 24], [1, 26], [1, 28], [2, 3], [2, 7], [2, 8], [2, 10], [2, 11], [2, 12], [2, 16], [2, 17], [2, 20], [2,... | null | null | null | {"colors": [0, 1, 0, 2, 2, 1, 0, 3, 3, 4, 1, 2, 4, 1, 5, 3, 1, 5, 4, 4, 2, 5, 1, 0, 4, 5, 2, 1, 4, 3]} | 1 |
construct-rlve-min-chromatic-number-l6-s7 | construct | rlve_min_chromatic_number | graph_k_coloring_chromatic | graph_theory | competition | 6 | RLVE-Gym/minimum_chromatic_number | MIT | [
"agentic_trivial",
"np_search"
] | An undirected simple graph has 30 vertices labelled 0..29 and edge list
[[0, 2], [0, 7], [0, 8], [0, 10], [0, 11], [0, 12], [0, 14], [0, 16], [0, 17], [0, 19], [0, 20], [0, 21], [0, 23], [0, 24], [1, 6], [1, 10], [1, 14], [1, 19], [1, 22], [2, 7], [2, 8], [2, 9], [2, 10], [2, 11], [2, 15], [2, 20], [2, 23], [2, 24], [2... | {"n": 30, "k": 6, "edges": [[0, 2], [0, 7], [0, 8], [0, 10], [0, 11], [0, 12], [0, 14], [0, 16], [0, 17], [0, 19], [0, 20], [0, 21], [0, 23], [0, 24], [1, 6], [1, 10], [1, 14], [1, 19], [1, 22], [2, 7], [2, 8], [2, 9], [2, 10], [2, 11], [2, 15], [2, 20], [2, 23], [2, 24], [2, 27], [3, 4], [3, 5], [3, 7], [3, 9], [3, 13... | null | null | null | {"colors": [0, 0, 1, 0, 1, 2, 1, 3, 3, 2, 3, 4, 1, 2, 5, 3, 4, 4, 2, 1, 5, 5, 1, 4, 5, 0, 2, 0, 4, 1]} | 1 |
construct-rlve-min-chromatic-number-l6-s8 | construct | rlve_min_chromatic_number | graph_k_coloring_chromatic | graph_theory | competition | 6 | RLVE-Gym/minimum_chromatic_number | MIT | [
"agentic_trivial",
"np_search"
] | An undirected simple graph has 30 vertices labelled 0..29 and edge list
[[0, 1], [0, 3], [0, 5], [0, 6], [0, 7], [0, 8], [0, 10], [0, 15], [0, 16], [0, 17], [0, 19], [0, 21], [0, 25], [0, 26], [0, 28], [1, 4], [1, 10], [1, 11], [1, 12], [1, 14], [1, 15], [1, 16], [1, 21], [1, 22], [1, 24], [1, 26], [2, 7], [2, 9], [2, ... | {"n": 30, "k": 6, "edges": [[0, 1], [0, 3], [0, 5], [0, 6], [0, 7], [0, 8], [0, 10], [0, 15], [0, 16], [0, 17], [0, 19], [0, 21], [0, 25], [0, 26], [0, 28], [1, 4], [1, 10], [1, 11], [1, 12], [1, 14], [1, 15], [1, 16], [1, 21], [1, 22], [1, 24], [1, 26], [2, 7], [2, 9], [2, 10], [2, 13], [2, 14], [2, 15], [2, 18], [2, ... | null | null | null | {"colors": [0, 1, 1, 2, 0, 3, 1, 4, 3, 0, 2, 2, 3, 3, 3, 4, 2, 1, 0, 5, 0, 5, 0, 1, 2, 1, 4, 5, 1, 1]} | 1 |
construct-rlve-min-chromatic-number-l6-s9 | construct | rlve_min_chromatic_number | graph_k_coloring_chromatic | graph_theory | competition | 6 | RLVE-Gym/minimum_chromatic_number | MIT | [
"agentic_trivial",
"np_search"
] | An undirected simple graph has 30 vertices labelled 0..29 and edge list
[[0, 4], [0, 9], [0, 14], [0, 17], [0, 18], [0, 19], [0, 22], [0, 24], [0, 25], [0, 26], [0, 28], [0, 29], [1, 3], [1, 5], [1, 8], [1, 19], [1, 21], [1, 23], [1, 27], [2, 4], [2, 5], [2, 7], [2, 8], [2, 9], [2, 11], [2, 13], [2, 14], [2, 15], [2, 1... | {"n": 30, "k": 7, "edges": [[0, 4], [0, 9], [0, 14], [0, 17], [0, 18], [0, 19], [0, 22], [0, 24], [0, 25], [0, 26], [0, 28], [0, 29], [1, 3], [1, 5], [1, 8], [1, 19], [1, 21], [1, 23], [1, 27], [2, 4], [2, 5], [2, 7], [2, 8], [2, 9], [2, 11], [2, 13], [2, 14], [2, 15], [2, 17], [2, 19], [2, 20], [2, 21], [2, 24], [2, 2... | null | null | null | {"colors": [0, 0, 0, 1, 1, 2, 0, 2, 1, 3, 0, 4, 0, 5, 1, 2, 1, 3, 4, 6, 3, 2, 6, 3, 3, 6, 5, 5, 4, 4]} | 1 |
construct-rlve-min-harmonious-coloring-l1-s0 | construct | rlve_min_harmonious_coloring | harmonious_chromatic_number | graph_theory | competition | 1 | RLVE-Gym/minimum_harmonious_chromatic_number | MIT | [
"agentic_trivial",
"np_search"
] | An undirected simple graph has 6 vertices labelled 0..5 and edge list
[[0, 1], [0, 4], [0, 5], [3, 4]]
A harmonious colouring assigns colours so that (1) adjacent vertices get different colours and (2) for every unordered pair of distinct colours {x, y} there is at most one edge whose endpoints are coloured x and y. T... | {"n": 6, "k": 4, "edges": [[0, 1], [0, 4], [0, 5], [3, 4]], "family": "rlve_min_harmonious_coloring", "subset": "construct"} | null | null | null | {"colors": [0, 1, 0, 1, 2, 3]} | 1 |
construct-rlve-min-harmonious-coloring-l1-s1 | construct | rlve_min_harmonious_coloring | harmonious_chromatic_number | graph_theory | competition | 1 | RLVE-Gym/minimum_harmonious_chromatic_number | MIT | [
"agentic_trivial",
"np_search"
] | An undirected simple graph has 6 vertices labelled 0..5 and edge list
[[0, 3], [0, 5], [2, 4]]
A harmonious colouring assigns colours so that (1) adjacent vertices get different colours and (2) for every unordered pair of distinct colours {x, y} there is at most one edge whose endpoints are coloured x and y. The minim... | {"n": 6, "k": 3, "edges": [[0, 3], [0, 5], [2, 4]], "family": "rlve_min_harmonious_coloring", "subset": "construct"} | null | null | null | {"colors": [0, 0, 1, 1, 2, 2]} | 1 |
construct-rlve-min-harmonious-coloring-l1-s2 | construct | rlve_min_harmonious_coloring | harmonious_chromatic_number | graph_theory | competition | 1 | RLVE-Gym/minimum_harmonious_chromatic_number | MIT | [
"agentic_trivial",
"np_search"
] | An undirected simple graph has 6 vertices labelled 0..5 and edge list
[[0, 3], [0, 4], [1, 2], [3, 5]]
A harmonious colouring assigns colours so that (1) adjacent vertices get different colours and (2) for every unordered pair of distinct colours {x, y} there is at most one edge whose endpoints are coloured x and y. T... | {"n": 6, "k": 4, "edges": [[0, 3], [0, 4], [1, 2], [3, 5]], "family": "rlve_min_harmonious_coloring", "subset": "construct"} | null | null | null | {"colors": [0, 0, 1, 2, 3, 1]} | 1 |
construct-rlve-min-harmonious-coloring-l1-s3 | construct | rlve_min_harmonious_coloring | harmonious_chromatic_number | graph_theory | competition | 1 | RLVE-Gym/minimum_harmonious_chromatic_number | MIT | [
"agentic_trivial",
"np_search"
] | An undirected simple graph has 6 vertices labelled 0..5 and edge list
[[0, 1], [0, 3], [0, 5], [2, 5]]
A harmonious colouring assigns colours so that (1) adjacent vertices get different colours and (2) for every unordered pair of distinct colours {x, y} there is at most one edge whose endpoints are coloured x and y. T... | {"n": 6, "k": 4, "edges": [[0, 1], [0, 3], [0, 5], [2, 5]], "family": "rlve_min_harmonious_coloring", "subset": "construct"} | null | null | null | {"colors": [0, 1, 1, 2, 0, 3]} | 1 |
construct-rlve-min-harmonious-coloring-l1-s4 | construct | rlve_min_harmonious_coloring | harmonious_chromatic_number | graph_theory | competition | 1 | RLVE-Gym/minimum_harmonious_chromatic_number | MIT | [
"agentic_trivial",
"np_search"
] | An undirected simple graph has 6 vertices labelled 0..5 and edge list
[[0, 3], [2, 4], [3, 5]]
A harmonious colouring assigns colours so that (1) adjacent vertices get different colours and (2) for every unordered pair of distinct colours {x, y} there is at most one edge whose endpoints are coloured x and y. The minim... | {"n": 6, "k": 3, "edges": [[0, 3], [2, 4], [3, 5]], "family": "rlve_min_harmonious_coloring", "subset": "construct"} | null | null | null | {"colors": [0, 0, 0, 1, 2, 2]} | 1 |
construct-rlve-min-harmonious-coloring-l1-s5 | construct | rlve_min_harmonious_coloring | harmonious_chromatic_number | graph_theory | competition | 1 | RLVE-Gym/minimum_harmonious_chromatic_number | MIT | [
"agentic_trivial",
"np_search"
] | An undirected simple graph has 6 vertices labelled 0..5 and edge list
[[0, 3], [1, 2], [1, 5]]
A harmonious colouring assigns colours so that (1) adjacent vertices get different colours and (2) for every unordered pair of distinct colours {x, y} there is at most one edge whose endpoints are coloured x and y. The minim... | {"n": 6, "k": 3, "edges": [[0, 3], [1, 2], [1, 5]], "family": "rlve_min_harmonious_coloring", "subset": "construct"} | null | null | null | {"colors": [0, 1, 0, 2, 0, 2]} | 1 |
construct-rlve-min-harmonious-coloring-l1-s6 | construct | rlve_min_harmonious_coloring | harmonious_chromatic_number | graph_theory | competition | 1 | RLVE-Gym/minimum_harmonious_chromatic_number | MIT | [
"agentic_trivial",
"np_search"
] | An undirected simple graph has 6 vertices labelled 0..5 and edge list
[[0, 4], [0, 5]]
A harmonious colouring assigns colours so that (1) adjacent vertices get different colours and (2) for every unordered pair of distinct colours {x, y} there is at most one edge whose endpoints are coloured x and y. The minimum numbe... | {"n": 6, "k": 3, "edges": [[0, 4], [0, 5]], "family": "rlve_min_harmonious_coloring", "subset": "construct"} | null | null | null | {"colors": [0, 0, 0, 0, 1, 2]} | 1 |
construct-rlve-min-harmonious-coloring-l1-s7 | construct | rlve_min_harmonious_coloring | harmonious_chromatic_number | graph_theory | competition | 1 | RLVE-Gym/minimum_harmonious_chromatic_number | MIT | [
"agentic_trivial",
"np_search"
] | An undirected simple graph has 6 vertices labelled 0..5 and edge list
[[0, 5], [2, 4], [3, 4], [4, 5]]
A harmonious colouring assigns colours so that (1) adjacent vertices get different colours and (2) for every unordered pair of distinct colours {x, y} there is at most one edge whose endpoints are coloured x and y. T... | {"n": 6, "k": 4, "edges": [[0, 5], [2, 4], [3, 4], [4, 5]], "family": "rlve_min_harmonious_coloring", "subset": "construct"} | null | null | null | {"colors": [0, 0, 0, 1, 2, 3]} | 1 |
construct-rlve-min-harmonious-coloring-l1-s8 | construct | rlve_min_harmonious_coloring | harmonious_chromatic_number | graph_theory | competition | 1 | RLVE-Gym/minimum_harmonious_chromatic_number | MIT | [
"agentic_trivial",
"np_search"
] | An undirected simple graph has 6 vertices labelled 0..5 and edge list
[[0, 4], [2, 3], [3, 4]]
A harmonious colouring assigns colours so that (1) adjacent vertices get different colours and (2) for every unordered pair of distinct colours {x, y} there is at most one edge whose endpoints are coloured x and y. The minim... | {"n": 6, "k": 3, "edges": [[0, 4], [2, 3], [3, 4]], "family": "rlve_min_harmonious_coloring", "subset": "construct"} | null | null | null | {"colors": [0, 0, 0, 1, 2, 0]} | 1 |
construct-rlve-min-harmonious-coloring-l1-s9 | construct | rlve_min_harmonious_coloring | harmonious_chromatic_number | graph_theory | competition | 1 | RLVE-Gym/minimum_harmonious_chromatic_number | MIT | [
"agentic_trivial",
"np_search"
] | An undirected simple graph has 6 vertices labelled 0..5 and edge list
[[0, 2], [0, 5], [2, 5], [3, 4]]
A harmonious colouring assigns colours so that (1) adjacent vertices get different colours and (2) for every unordered pair of distinct colours {x, y} there is at most one edge whose endpoints are coloured x and y. T... | {"n": 6, "k": 4, "edges": [[0, 2], [0, 5], [2, 5], [3, 4]], "family": "rlve_min_harmonious_coloring", "subset": "construct"} | null | null | null | {"colors": [0, 0, 1, 0, 2, 3]} | 1 |
construct-rlve-min-harmonious-coloring-l2-s0 | construct | rlve_min_harmonious_coloring | harmonious_chromatic_number | graph_theory | competition | 2 | RLVE-Gym/minimum_harmonious_chromatic_number | MIT | [
"agentic_trivial",
"np_search"
] | An undirected simple graph has 8 vertices labelled 0..7 and edge list
[[0, 4], [1, 4], [1, 5], [1, 6], [2, 7], [4, 6], [4, 7], [6, 7]]
A harmonious colouring assigns colours so that (1) adjacent vertices get different colours and (2) for every unordered pair of distinct colours {x, y} there is at most one edge whose e... | {"n": 8, "k": 5, "edges": [[0, 4], [1, 4], [1, 5], [1, 6], [2, 7], [4, 6], [4, 7], [6, 7]], "family": "rlve_min_harmonious_coloring", "subset": "construct"} | null | null | null | {"colors": [0, 1, 0, 0, 2, 0, 3, 4]} | 1 |
construct-rlve-min-harmonious-coloring-l2-s1 | construct | rlve_min_harmonious_coloring | harmonious_chromatic_number | graph_theory | competition | 2 | RLVE-Gym/minimum_harmonious_chromatic_number | MIT | [
"agentic_trivial",
"np_search"
] | An undirected simple graph has 8 vertices labelled 0..7 and edge list
[[1, 6], [2, 3], [2, 5], [3, 5], [3, 6], [3, 7], [4, 5], [4, 7]]
A harmonious colouring assigns colours so that (1) adjacent vertices get different colours and (2) for every unordered pair of distinct colours {x, y} there is at most one edge whose e... | {"n": 8, "k": 5, "edges": [[1, 6], [2, 3], [2, 5], [3, 5], [3, 6], [3, 7], [4, 5], [4, 7]], "family": "rlve_min_harmonious_coloring", "subset": "construct"} | null | null | null | {"colors": [0, 0, 0, 1, 2, 3, 2, 4]} | 1 |
construct-rlve-min-harmonious-coloring-l2-s2 | construct | rlve_min_harmonious_coloring | harmonious_chromatic_number | graph_theory | competition | 2 | RLVE-Gym/minimum_harmonious_chromatic_number | MIT | [
"agentic_trivial",
"np_search"
] | An undirected simple graph has 8 vertices labelled 0..7 and edge list
[[2, 5], [5, 7]]
A harmonious colouring assigns colours so that (1) adjacent vertices get different colours and (2) for every unordered pair of distinct colours {x, y} there is at most one edge whose endpoints are coloured x and y. The minimum numbe... | {"n": 8, "k": 3, "edges": [[2, 5], [5, 7]], "family": "rlve_min_harmonious_coloring", "subset": "construct"} | null | null | null | {"colors": [0, 0, 0, 0, 0, 1, 0, 2]} | 1 |
construct-rlve-min-harmonious-coloring-l2-s3 | construct | rlve_min_harmonious_coloring | harmonious_chromatic_number | graph_theory | competition | 2 | RLVE-Gym/minimum_harmonious_chromatic_number | MIT | [
"agentic_trivial",
"np_search"
] | An undirected simple graph has 8 vertices labelled 0..7 and edge list
[[2, 4], [3, 4], [3, 6], [3, 7], [5, 7]]
A harmonious colouring assigns colours so that (1) adjacent vertices get different colours and (2) for every unordered pair of distinct colours {x, y} there is at most one edge whose endpoints are coloured x ... | {"n": 8, "k": 4, "edges": [[2, 4], [3, 4], [3, 6], [3, 7], [5, 7]], "family": "rlve_min_harmonious_coloring", "subset": "construct"} | null | null | null | {"colors": [0, 0, 0, 1, 2, 0, 0, 3]} | 1 |
construct-rlve-min-harmonious-coloring-l2-s4 | construct | rlve_min_harmonious_coloring | harmonious_chromatic_number | graph_theory | competition | 2 | RLVE-Gym/minimum_harmonious_chromatic_number | MIT | [
"agentic_trivial",
"np_search"
] | An undirected simple graph has 8 vertices labelled 0..7 and edge list
[[0, 1], [0, 6], [3, 4], [3, 7], [5, 7]]
A harmonious colouring assigns colours so that (1) adjacent vertices get different colours and (2) for every unordered pair of distinct colours {x, y} there is at most one edge whose endpoints are coloured x ... | {"n": 8, "k": 4, "edges": [[0, 1], [0, 6], [3, 4], [3, 7], [5, 7]], "family": "rlve_min_harmonious_coloring", "subset": "construct"} | null | null | null | {"colors": [0, 1, 0, 1, 2, 0, 2, 3]} | 1 |
construct-rlve-min-harmonious-coloring-l2-s5 | construct | rlve_min_harmonious_coloring | harmonious_chromatic_number | graph_theory | competition | 2 | RLVE-Gym/minimum_harmonious_chromatic_number | MIT | [
"agentic_trivial",
"np_search"
] | An undirected simple graph has 8 vertices labelled 0..7 and edge list
[[0, 7], [1, 7], [2, 6], [2, 7], [4, 5]]
A harmonious colouring assigns colours so that (1) adjacent vertices get different colours and (2) for every unordered pair of distinct colours {x, y} there is at most one edge whose endpoints are coloured x ... | {"n": 8, "k": 4, "edges": [[0, 7], [1, 7], [2, 6], [2, 7], [4, 5]], "family": "rlve_min_harmonious_coloring", "subset": "construct"} | null | null | null | {"colors": [0, 1, 2, 0, 0, 1, 0, 3]} | 1 |
construct-rlve-min-harmonious-coloring-l2-s6 | construct | rlve_min_harmonious_coloring | harmonious_chromatic_number | graph_theory | competition | 2 | RLVE-Gym/minimum_harmonious_chromatic_number | MIT | [
"agentic_trivial",
"np_search"
] | An undirected simple graph has 8 vertices labelled 0..7 and edge list
[[0, 1], [0, 2], [1, 4], [2, 7]]
A harmonious colouring assigns colours so that (1) adjacent vertices get different colours and (2) for every unordered pair of distinct colours {x, y} there is at most one edge whose endpoints are coloured x and y. T... | {"n": 8, "k": 4, "edges": [[0, 1], [0, 2], [1, 4], [2, 7]], "family": "rlve_min_harmonious_coloring", "subset": "construct"} | null | null | null | {"colors": [0, 1, 2, 0, 2, 0, 0, 3]} | 1 |
construct-rlve-min-harmonious-coloring-l2-s7 | construct | rlve_min_harmonious_coloring | harmonious_chromatic_number | graph_theory | competition | 2 | RLVE-Gym/minimum_harmonious_chromatic_number | MIT | [
"agentic_trivial",
"np_search"
] | An undirected simple graph has 8 vertices labelled 0..7 and edge list
[[0, 4], [0, 6], [1, 3], [1, 7], [2, 4], [2, 5], [3, 7]]
A harmonious colouring assigns colours so that (1) adjacent vertices get different colours and (2) for every unordered pair of distinct colours {x, y} there is at most one edge whose endpoints... | {"n": 8, "k": 5, "edges": [[0, 4], [0, 6], [1, 3], [1, 7], [2, 4], [2, 5], [3, 7]], "family": "rlve_min_harmonious_coloring", "subset": "construct"} | null | null | null | {"colors": [0, 0, 1, 1, 2, 3, 3, 4]} | 1 |
construct-rlve-min-harmonious-coloring-l2-s8 | construct | rlve_min_harmonious_coloring | harmonious_chromatic_number | graph_theory | competition | 2 | RLVE-Gym/minimum_harmonious_chromatic_number | MIT | [
"agentic_trivial",
"np_search"
] | An undirected simple graph has 8 vertices labelled 0..7 and edge list
[[1, 2], [1, 4], [1, 6], [2, 4], [2, 6], [3, 4], [5, 6]]
A harmonious colouring assigns colours so that (1) adjacent vertices get different colours and (2) for every unordered pair of distinct colours {x, y} there is at most one edge whose endpoints... | {"n": 8, "k": 5, "edges": [[1, 2], [1, 4], [1, 6], [2, 4], [2, 6], [3, 4], [5, 6]], "family": "rlve_min_harmonious_coloring", "subset": "construct"} | null | null | null | {"colors": [0, 0, 1, 2, 3, 2, 4, 0]} | 1 |
construct-rlve-min-harmonious-coloring-l2-s9 | construct | rlve_min_harmonious_coloring | harmonious_chromatic_number | graph_theory | competition | 2 | RLVE-Gym/minimum_harmonious_chromatic_number | MIT | [
"agentic_trivial",
"np_search"
] | An undirected simple graph has 8 vertices labelled 0..7 and edge list
[[1, 3], [4, 5]]
A harmonious colouring assigns colours so that (1) adjacent vertices get different colours and (2) for every unordered pair of distinct colours {x, y} there is at most one edge whose endpoints are coloured x and y. The minimum numbe... | {"n": 8, "k": 3, "edges": [[1, 3], [4, 5]], "family": "rlve_min_harmonious_coloring", "subset": "construct"} | null | null | null | {"colors": [0, 0, 0, 1, 0, 2, 0, 0]} | 1 |
construct-rlve-min-harmonious-coloring-l3-s0 | construct | rlve_min_harmonious_coloring | harmonious_chromatic_number | graph_theory | competition | 3 | RLVE-Gym/minimum_harmonious_chromatic_number | MIT | [
"agentic_trivial",
"np_search"
] | An undirected simple graph has 10 vertices labelled 0..9 and edge list
[[0, 3], [5, 6], [5, 8], [6, 9]]
A harmonious colouring assigns colours so that (1) adjacent vertices get different colours and (2) for every unordered pair of distinct colours {x, y} there is at most one edge whose endpoints are coloured x and y. ... | {"n": 10, "k": 4, "edges": [[0, 3], [5, 6], [5, 8], [6, 9]], "family": "rlve_min_harmonious_coloring", "subset": "construct"} | null | null | null | {"colors": [0, 0, 0, 1, 0, 0, 2, 0, 3, 1]} | 1 |
construct-rlve-min-harmonious-coloring-l3-s1 | construct | rlve_min_harmonious_coloring | harmonious_chromatic_number | graph_theory | competition | 3 | RLVE-Gym/minimum_harmonious_chromatic_number | MIT | [
"agentic_trivial",
"np_search"
] | An undirected simple graph has 10 vertices labelled 0..9 and edge list
[[2, 5], [3, 4], [3, 7], [4, 5], [4, 9], [5, 8]]
A harmonious colouring assigns colours so that (1) adjacent vertices get different colours and (2) for every unordered pair of distinct colours {x, y} there is at most one edge whose endpoints are co... | {"n": 10, "k": 4, "edges": [[2, 5], [3, 4], [3, 7], [4, 5], [4, 9], [5, 8]], "family": "rlve_min_harmonious_coloring", "subset": "construct"} | null | null | null | {"colors": [0, 0, 0, 0, 1, 2, 0, 3, 3, 3]} | 1 |
construct-rlve-min-harmonious-coloring-l3-s2 | construct | rlve_min_harmonious_coloring | harmonious_chromatic_number | graph_theory | competition | 3 | RLVE-Gym/minimum_harmonious_chromatic_number | MIT | [
"agentic_trivial",
"np_search"
] | An undirected simple graph has 10 vertices labelled 0..9 and edge list
[[0, 8], [0, 9], [1, 7], [1, 8], [2, 8], [3, 5], [4, 6], [5, 7], [6, 7], [6, 9], [7, 9]]
A harmonious colouring assigns colours so that (1) adjacent vertices get different colours and (2) for every unordered pair of distinct colours {x, y} there is... | {"n": 10, "k": 6, "edges": [[0, 8], [0, 9], [1, 7], [1, 8], [2, 8], [3, 5], [4, 6], [5, 7], [6, 7], [6, 9], [7, 9]], "family": "rlve_min_harmonious_coloring", "subset": "construct"} | null | null | null | {"colors": [0, 1, 2, 1, 0, 0, 2, 3, 4, 5]} | 1 |
construct-rlve-min-harmonious-coloring-l3-s3 | construct | rlve_min_harmonious_coloring | harmonious_chromatic_number | graph_theory | competition | 3 | RLVE-Gym/minimum_harmonious_chromatic_number | MIT | [
"agentic_trivial",
"np_search"
] | An undirected simple graph has 10 vertices labelled 0..9 and edge list
[[0, 3], [0, 8], [1, 8], [7, 9]]
A harmonious colouring assigns colours so that (1) adjacent vertices get different colours and (2) for every unordered pair of distinct colours {x, y} there is at most one edge whose endpoints are coloured x and y. ... | {"n": 10, "k": 4, "edges": [[0, 3], [0, 8], [1, 8], [7, 9]], "family": "rlve_min_harmonious_coloring", "subset": "construct"} | null | null | null | {"colors": [0, 1, 0, 1, 0, 0, 0, 0, 2, 3]} | 1 |
construct-rlve-min-harmonious-coloring-l3-s4 | construct | rlve_min_harmonious_coloring | harmonious_chromatic_number | graph_theory | competition | 3 | RLVE-Gym/minimum_harmonious_chromatic_number | MIT | [
"agentic_trivial",
"np_search"
] | An undirected simple graph has 10 vertices labelled 0..9 and edge list
[[0, 9], [1, 5], [1, 7], [1, 9], [2, 7], [3, 5], [3, 6], [3, 7], [4, 5], [4, 8], [7, 9]]
A harmonious colouring assigns colours so that (1) adjacent vertices get different colours and (2) for every unordered pair of distinct colours {x, y} there is... | {"n": 10, "k": 6, "edges": [[0, 9], [1, 5], [1, 7], [1, 9], [2, 7], [3, 5], [3, 6], [3, 7], [4, 5], [4, 8], [7, 9]], "family": "rlve_min_harmonious_coloring", "subset": "construct"} | null | null | null | {"colors": [0, 1, 0, 2, 0, 3, 0, 4, 1, 5]} | 1 |
construct-rlve-min-harmonious-coloring-l3-s5 | construct | rlve_min_harmonious_coloring | harmonious_chromatic_number | graph_theory | competition | 3 | RLVE-Gym/minimum_harmonious_chromatic_number | MIT | [
"agentic_trivial",
"np_search"
] | An undirected simple graph has 10 vertices labelled 0..9 and edge list
[[0, 3], [0, 9], [1, 9], [2, 8]]
A harmonious colouring assigns colours so that (1) adjacent vertices get different colours and (2) for every unordered pair of distinct colours {x, y} there is at most one edge whose endpoints are coloured x and y. ... | {"n": 10, "k": 4, "edges": [[0, 3], [0, 9], [1, 9], [2, 8]], "family": "rlve_min_harmonious_coloring", "subset": "construct"} | null | null | null | {"colors": [0, 1, 0, 1, 0, 0, 0, 0, 2, 3]} | 1 |
construct-rlve-min-harmonious-coloring-l3-s6 | construct | rlve_min_harmonious_coloring | harmonious_chromatic_number | graph_theory | competition | 3 | RLVE-Gym/minimum_harmonious_chromatic_number | MIT | [
"agentic_trivial",
"np_search"
] | An undirected simple graph has 10 vertices labelled 0..9 and edge list
[[1, 6], [2, 6], [2, 9], [3, 4], [3, 6], [3, 7], [5, 9], [6, 9], [7, 8]]
A harmonious colouring assigns colours so that (1) adjacent vertices get different colours and (2) for every unordered pair of distinct colours {x, y} there is at most one edg... | {"n": 10, "k": 5, "edges": [[1, 6], [2, 6], [2, 9], [3, 4], [3, 6], [3, 7], [5, 9], [6, 9], [7, 8]], "family": "rlve_min_harmonious_coloring", "subset": "construct"} | null | null | null | {"colors": [0, 0, 1, 2, 0, 0, 3, 1, 0, 4]} | 1 |
construct-rlve-min-harmonious-coloring-l3-s7 | construct | rlve_min_harmonious_coloring | harmonious_chromatic_number | graph_theory | competition | 3 | RLVE-Gym/minimum_harmonious_chromatic_number | MIT | [
"agentic_trivial",
"np_search"
] | An undirected simple graph has 10 vertices labelled 0..9 and edge list
[[0, 1], [2, 6], [3, 5], [5, 8]]
A harmonious colouring assigns colours so that (1) adjacent vertices get different colours and (2) for every unordered pair of distinct colours {x, y} there is at most one edge whose endpoints are coloured x and y. ... | {"n": 10, "k": 4, "edges": [[0, 1], [2, 6], [3, 5], [5, 8]], "family": "rlve_min_harmonious_coloring", "subset": "construct"} | null | null | null | {"colors": [0, 1, 0, 0, 0, 2, 3, 0, 1, 0]} | 1 |
construct-rlve-min-harmonious-coloring-l3-s8 | construct | rlve_min_harmonious_coloring | harmonious_chromatic_number | graph_theory | competition | 3 | RLVE-Gym/minimum_harmonious_chromatic_number | MIT | [
"agentic_trivial",
"np_search"
] | An undirected simple graph has 10 vertices labelled 0..9 and edge list
[[0, 3], [1, 3], [2, 4], [5, 6], [6, 9], [8, 9]]
A harmonious colouring assigns colours so that (1) adjacent vertices get different colours and (2) for every unordered pair of distinct colours {x, y} there is at most one edge whose endpoints are co... | {"n": 10, "k": 4, "edges": [[0, 3], [1, 3], [2, 4], [5, 6], [6, 9], [8, 9]], "family": "rlve_min_harmonious_coloring", "subset": "construct"} | null | null | null | {"colors": [0, 1, 0, 2, 3, 0, 1, 0, 2, 3]} | 1 |
construct-rlve-min-harmonious-coloring-l3-s9 | construct | rlve_min_harmonious_coloring | harmonious_chromatic_number | graph_theory | competition | 3 | RLVE-Gym/minimum_harmonious_chromatic_number | MIT | [
"agentic_trivial",
"np_search"
] | An undirected simple graph has 10 vertices labelled 0..9 and edge list
[[0, 3], [0, 6], [0, 9], [1, 5], [1, 9], [2, 5], [2, 7], [3, 4], [4, 5], [4, 6], [6, 7], [6, 8], [8, 9]]
A harmonious colouring assigns colours so that (1) adjacent vertices get different colours and (2) for every unordered pair of distinct colours... | {"n": 10, "k": 7, "edges": [[0, 3], [0, 6], [0, 9], [1, 5], [1, 9], [2, 5], [2, 7], [3, 4], [4, 5], [4, 6], [6, 7], [6, 8], [8, 9]], "family": "rlve_min_harmonious_coloring", "subset": "construct"} | null | null | null | {"colors": [0, 1, 0, 1, 2, 3, 4, 5, 3, 6]} | 1 |
construct-rlve-min-harmonious-coloring-l4-s0 | construct | rlve_min_harmonious_coloring | harmonious_chromatic_number | graph_theory | competition | 4 | RLVE-Gym/minimum_harmonious_chromatic_number | MIT | [
"agentic_trivial",
"np_search"
] | An undirected simple graph has 12 vertices labelled 0..11 and edge list
[[1, 6], [3, 6], [3, 9], [3, 10], [4, 11], [5, 8], [6, 7], [9, 11], [10, 11]]
A harmonious colouring assigns colours so that (1) adjacent vertices get different colours and (2) for every unordered pair of distinct colours {x, y} there is at most o... | {"n": 12, "k": 5, "edges": [[1, 6], [3, 6], [3, 9], [3, 10], [4, 11], [5, 8], [6, 7], [9, 11], [10, 11]], "family": "rlve_min_harmonious_coloring", "subset": "construct"} | null | null | null | {"colors": [0, 0, 0, 1, 1, 0, 2, 3, 3, 0, 3, 4]} | 1 |
construct-rlve-min-harmonious-coloring-l4-s1 | construct | rlve_min_harmonious_coloring | harmonious_chromatic_number | graph_theory | competition | 4 | RLVE-Gym/minimum_harmonious_chromatic_number | MIT | [
"agentic_trivial",
"np_search"
] | An undirected simple graph has 12 vertices labelled 0..11 and edge list
[[0, 2], [0, 4], [0, 6], [0, 11], [1, 4], [1, 10], [2, 4], [2, 5], [2, 11], [3, 7], [3, 9], [4, 8], [4, 11], [5, 8], [5, 10], [6, 7]]
A harmonious colouring assigns colours so that (1) adjacent vertices get different colours and (2) for every unor... | {"n": 12, "k": 7, "edges": [[0, 2], [0, 4], [0, 6], [0, 11], [1, 4], [1, 10], [2, 4], [2, 5], [2, 11], [3, 7], [3, 9], [4, 8], [4, 11], [5, 8], [5, 10], [6, 7]], "family": "rlve_min_harmonious_coloring", "subset": "construct"} | null | null | null | {"colors": [0, 1, 2, 0, 3, 4, 1, 4, 5, 5, 6, 6]} | 1 |
construct-rlve-min-harmonious-coloring-l4-s2 | construct | rlve_min_harmonious_coloring | harmonious_chromatic_number | graph_theory | competition | 4 | RLVE-Gym/minimum_harmonious_chromatic_number | MIT | [
"agentic_trivial",
"np_search"
] | An undirected simple graph has 12 vertices labelled 0..11 and edge list
[[0, 6], [0, 10], [1, 3], [1, 8], [1, 11], [4, 8], [5, 7], [5, 11], [7, 10]]
A harmonious colouring assigns colours so that (1) adjacent vertices get different colours and (2) for every unordered pair of distinct colours {x, y} there is at most on... | {"n": 12, "k": 5, "edges": [[0, 6], [0, 10], [1, 3], [1, 8], [1, 11], [4, 8], [5, 7], [5, 11], [7, 10]], "family": "rlve_min_harmonious_coloring", "subset": "construct"} | null | null | null | {"colors": [0, 1, 0, 0, 0, 2, 2, 3, 3, 0, 4, 4]} | 1 |
construct-rlve-min-harmonious-coloring-l4-s3 | construct | rlve_min_harmonious_coloring | harmonious_chromatic_number | graph_theory | competition | 4 | RLVE-Gym/minimum_harmonious_chromatic_number | MIT | [
"agentic_trivial",
"np_search"
] | An undirected simple graph has 12 vertices labelled 0..11 and edge list
[[0, 3], [1, 11], [2, 5], [2, 8], [3, 8], [3, 11], [4, 5], [4, 6], [4, 7], [4, 11], [7, 9], [7, 11], [9, 11]]
A harmonious colouring assigns colours so that (1) adjacent vertices get different colours and (2) for every unordered pair of distinct c... | {"n": 12, "k": 6, "edges": [[0, 3], [1, 11], [2, 5], [2, 8], [3, 8], [3, 11], [4, 5], [4, 6], [4, 7], [4, 11], [7, 9], [7, 11], [9, 11]], "family": "rlve_min_harmonious_coloring", "subset": "construct"} | null | null | null | {"colors": [0, 0, 0, 1, 2, 3, 0, 4, 4, 3, 0, 5]} | 1 |
construct-rlve-min-harmonious-coloring-l4-s4 | construct | rlve_min_harmonious_coloring | harmonious_chromatic_number | graph_theory | competition | 4 | RLVE-Gym/minimum_harmonious_chromatic_number | MIT | [
"agentic_trivial",
"np_search"
] | An undirected simple graph has 12 vertices labelled 0..11 and edge list
[[0, 5], [1, 5], [2, 11], [4, 9], [5, 10], [6, 9]]
A harmonious colouring assigns colours so that (1) adjacent vertices get different colours and (2) for every unordered pair of distinct colours {x, y} there is at most one edge whose endpoints are... | {"n": 12, "k": 4, "edges": [[0, 5], [1, 5], [2, 11], [4, 9], [5, 10], [6, 9]], "family": "rlve_min_harmonious_coloring", "subset": "construct"} | null | null | null | {"colors": [0, 1, 0, 0, 0, 2, 1, 0, 0, 3, 3, 1]} | 1 |
construct-rlve-min-harmonious-coloring-l4-s5 | construct | rlve_min_harmonious_coloring | harmonious_chromatic_number | graph_theory | competition | 4 | RLVE-Gym/minimum_harmonious_chromatic_number | MIT | [
"agentic_trivial",
"np_search"
] | An undirected simple graph has 12 vertices labelled 0..11 and edge list
[[0, 4], [0, 11], [2, 9], [3, 9], [4, 11], [5, 7], [6, 9], [7, 11], [8, 11]]
A harmonious colouring assigns colours so that (1) adjacent vertices get different colours and (2) for every unordered pair of distinct colours {x, y} there is at most on... | {"n": 12, "k": 5, "edges": [[0, 4], [0, 11], [2, 9], [3, 9], [4, 11], [5, 7], [6, 9], [7, 11], [8, 11]], "family": "rlve_min_harmonious_coloring", "subset": "construct"} | null | null | null | {"colors": [0, 0, 0, 1, 1, 0, 2, 2, 3, 3, 0, 4]} | 1 |
construct-rlve-min-harmonious-coloring-l4-s6 | construct | rlve_min_harmonious_coloring | harmonious_chromatic_number | graph_theory | competition | 4 | RLVE-Gym/minimum_harmonious_chromatic_number | MIT | [
"agentic_trivial",
"np_search"
] | An undirected simple graph has 12 vertices labelled 0..11 and edge list
[[0, 1], [1, 4], [1, 8], [2, 10], [3, 4], [3, 8], [6, 8], [7, 11], [9, 11]]
A harmonious colouring assigns colours so that (1) adjacent vertices get different colours and (2) for every unordered pair of distinct colours {x, y} there is at most one... | {"n": 12, "k": 5, "edges": [[0, 1], [1, 4], [1, 8], [2, 10], [3, 4], [3, 8], [6, 8], [7, 11], [9, 11]], "family": "rlve_min_harmonious_coloring", "subset": "construct"} | null | null | null | {"colors": [0, 1, 0, 0, 2, 0, 2, 1, 3, 2, 4, 4]} | 1 |
construct-rlve-min-harmonious-coloring-l4-s7 | construct | rlve_min_harmonious_coloring | harmonious_chromatic_number | graph_theory | competition | 4 | RLVE-Gym/minimum_harmonious_chromatic_number | MIT | [
"agentic_trivial",
"np_search"
] | An undirected simple graph has 12 vertices labelled 0..11 and edge list
[[1, 11], [3, 4], [3, 10], [4, 5], [7, 10], [8, 11]]
A harmonious colouring assigns colours so that (1) adjacent vertices get different colours and (2) for every unordered pair of distinct colours {x, y} there is at most one edge whose endpoints a... | {"n": 12, "k": 4, "edges": [[1, 11], [3, 4], [3, 10], [4, 5], [7, 10], [8, 11]], "family": "rlve_min_harmonious_coloring", "subset": "construct"} | null | null | null | {"colors": [0, 0, 0, 0, 1, 2, 0, 1, 3, 0, 3, 2]} | 1 |
construct-rlve-min-harmonious-coloring-l4-s8 | construct | rlve_min_harmonious_coloring | harmonious_chromatic_number | graph_theory | competition | 4 | RLVE-Gym/minimum_harmonious_chromatic_number | MIT | [
"agentic_trivial",
"np_search"
] | An undirected simple graph has 12 vertices labelled 0..11 and edge list
[[0, 2], [0, 7], [0, 10], [1, 2], [4, 9], [7, 9]]
A harmonious colouring assigns colours so that (1) adjacent vertices get different colours and (2) for every unordered pair of distinct colours {x, y} there is at most one edge whose endpoints are ... | {"n": 12, "k": 4, "edges": [[0, 2], [0, 7], [0, 10], [1, 2], [4, 9], [7, 9]], "family": "rlve_min_harmonious_coloring", "subset": "construct"} | null | null | null | {"colors": [0, 1, 2, 0, 2, 0, 0, 1, 0, 3, 3, 0]} | 1 |
construct-rlve-min-harmonious-coloring-l4-s9 | construct | rlve_min_harmonious_coloring | harmonious_chromatic_number | graph_theory | competition | 4 | RLVE-Gym/minimum_harmonious_chromatic_number | MIT | [
"agentic_trivial",
"np_search"
] | An undirected simple graph has 12 vertices labelled 0..11 and edge list
[[1, 4], [1, 7], [1, 10], [2, 4], [2, 8], [3, 4], [3, 6], [3, 7], [5, 8], [6, 7], [6, 9], [6, 10], [9, 11]]
A harmonious colouring assigns colours so that (1) adjacent vertices get different colours and (2) for every unordered pair of distinct col... | {"n": 12, "k": 6, "edges": [[1, 4], [1, 7], [1, 10], [2, 4], [2, 8], [3, 4], [3, 6], [3, 7], [5, 8], [6, 7], [6, 9], [6, 10], [9, 11]], "family": "rlve_min_harmonious_coloring", "subset": "construct"} | null | null | null | {"colors": [0, 0, 1, 2, 3, 0, 4, 5, 2, 3, 1, 5]} | 1 |
construct-rlve-min-harmonious-coloring-l5-s0 | construct | rlve_min_harmonious_coloring | harmonious_chromatic_number | graph_theory | competition | 5 | RLVE-Gym/minimum_harmonious_chromatic_number | MIT | [
"agentic_trivial",
"np_search"
] | An undirected simple graph has 15 vertices labelled 0..14 and edge list
[[0, 4], [0, 11], [1, 4], [1, 9], [1, 13], [2, 3], [2, 5], [2, 14], [3, 5], [4, 6], [4, 8], [4, 9], [5, 8], [5, 10], [5, 11], [5, 12], [5, 14], [6, 9], [6, 13], [6, 14], [7, 11], [9, 11], [10, 11], [10, 12], [11, 14], [12, 13]]
A harmonious colour... | {"n": 15, "k": 9, "edges": [[0, 4], [0, 11], [1, 4], [1, 9], [1, 13], [2, 3], [2, 5], [2, 14], [3, 5], [4, 6], [4, 8], [4, 9], [5, 8], [5, 10], [5, 11], [5, 12], [5, 14], [6, 9], [6, 13], [6, 14], [7, 11], [9, 11], [10, 11], [10, 12], [11, 14], [12, 13]], "family": "rlve_min_harmonious_coloring", "subset": "construct"} | null | null | null | {"colors": [0, 1, 0, 2, 3, 4, 2, 2, 5, 6, 3, 7, 8, 5, 1]} | 1 |
construct-rlve-min-harmonious-coloring-l5-s1 | construct | rlve_min_harmonious_coloring | harmonious_chromatic_number | graph_theory | competition | 5 | RLVE-Gym/minimum_harmonious_chromatic_number | MIT | [
"agentic_trivial",
"np_search"
] | An undirected simple graph has 15 vertices labelled 0..14 and edge list
[[0, 7], [1, 11], [1, 13], [2, 3], [2, 4], [2, 6], [2, 10], [2, 11], [2, 13], [3, 5], [3, 8], [3, 10], [3, 14], [5, 11], [6, 7], [6, 8], [6, 9], [7, 11], [7, 14], [8, 12], [8, 13], [9, 13], [9, 14], [10, 13], [11, 12], [11, 14]]
A harmonious colou... | {"n": 15, "k": 9, "edges": [[0, 7], [1, 11], [1, 13], [2, 3], [2, 4], [2, 6], [2, 10], [2, 11], [2, 13], [3, 5], [3, 8], [3, 10], [3, 14], [5, 11], [6, 7], [6, 8], [6, 9], [7, 11], [7, 14], [8, 12], [8, 13], [9, 13], [9, 14], [10, 13], [11, 12], [11, 14]], "family": "rlve_min_harmonious_coloring", "subset": "construct"... | null | null | null | {"colors": [0, 1, 2, 1, 0, 3, 3, 4, 0, 5, 4, 6, 5, 7, 8]} | 1 |
construct-rlve-min-harmonious-coloring-l5-s2 | construct | rlve_min_harmonious_coloring | harmonious_chromatic_number | graph_theory | competition | 5 | RLVE-Gym/minimum_harmonious_chromatic_number | MIT | [
"agentic_trivial",
"np_search"
] | An undirected simple graph has 15 vertices labelled 0..14 and edge list
[[0, 2], [0, 7], [0, 12], [1, 5], [1, 9], [2, 4], [2, 5], [2, 7], [2, 9], [3, 4], [3, 6], [3, 12], [4, 9], [4, 11], [5, 7], [5, 8], [5, 13], [6, 9], [6, 10], [6, 14], [7, 11], [7, 13], [10, 11], [10, 13], [12, 13], [12, 14]]
A harmonious colouring... | {"n": 15, "k": 9, "edges": [[0, 2], [0, 7], [0, 12], [1, 5], [1, 9], [2, 4], [2, 5], [2, 7], [2, 9], [3, 4], [3, 6], [3, 12], [4, 9], [4, 11], [5, 7], [5, 8], [5, 13], [6, 9], [6, 10], [6, 14], [7, 11], [7, 13], [10, 11], [10, 13], [12, 13], [12, 14]], "family": "rlve_min_harmonious_coloring", "subset": "construct"} | null | null | null | {"colors": [0, 0, 1, 2, 3, 2, 4, 5, 6, 7, 6, 8, 8, 7, 1]} | 1 |
construct-rlve-min-harmonious-coloring-l5-s3 | construct | rlve_min_harmonious_coloring | harmonious_chromatic_number | graph_theory | competition | 5 | RLVE-Gym/minimum_harmonious_chromatic_number | MIT | [
"agentic_trivial",
"np_search"
] | An undirected simple graph has 15 vertices labelled 0..14 and edge list
[[0, 3], [0, 5], [0, 8], [0, 9], [0, 11], [0, 13], [0, 14], [1, 4], [1, 6], [1, 7], [1, 10], [1, 11], [2, 3], [2, 10], [3, 4], [3, 8], [4, 5], [4, 11], [4, 13], [5, 8], [6, 10], [6, 13], [7, 8], [7, 13], [7, 14], [8, 14], [9, 12], [10, 13], [11, 12... | {"n": 15, "k": 10, "edges": [[0, 3], [0, 5], [0, 8], [0, 9], [0, 11], [0, 13], [0, 14], [1, 4], [1, 6], [1, 7], [1, 10], [1, 11], [2, 3], [2, 10], [3, 4], [3, 8], [4, 5], [4, 11], [4, 13], [5, 8], [6, 10], [6, 13], [7, 8], [7, 13], [7, 14], [8, 14], [9, 12], [10, 13], [11, 12], [12, 13], [12, 14]], "family": "rlve_min_... | null | null | null | {"colors": [0, 1, 2, 3, 4, 5, 3, 2, 6, 1, 5, 7, 8, 9, 4]} | 1 |
construct-rlve-min-harmonious-coloring-l5-s4 | construct | rlve_min_harmonious_coloring | harmonious_chromatic_number | graph_theory | competition | 5 | RLVE-Gym/minimum_harmonious_chromatic_number | MIT | [
"agentic_trivial",
"np_search"
] | An undirected simple graph has 15 vertices labelled 0..14 and edge list
[[0, 1], [0, 11], [1, 3], [1, 4], [1, 5], [1, 10], [2, 4], [2, 8], [2, 10], [2, 14], [3, 8], [3, 9], [3, 12], [4, 7], [5, 8], [5, 12], [6, 10], [6, 11], [7, 8], [7, 10], [9, 10]]
A harmonious colouring assigns colours so that (1) adjacent vertices... | {"n": 15, "k": 8, "edges": [[0, 1], [0, 11], [1, 3], [1, 4], [1, 5], [1, 10], [2, 4], [2, 8], [2, 10], [2, 14], [3, 8], [3, 9], [3, 12], [4, 7], [5, 8], [5, 12], [6, 10], [6, 11], [7, 8], [7, 10], [9, 10]], "family": "rlve_min_harmonious_coloring", "subset": "construct"} | null | null | null | {"colors": [0, 1, 0, 2, 3, 4, 2, 5, 6, 3, 7, 4, 5, 0, 2]} | 1 |
construct-rlve-min-harmonious-coloring-l5-s5 | construct | rlve_min_harmonious_coloring | harmonious_chromatic_number | graph_theory | competition | 5 | RLVE-Gym/minimum_harmonious_chromatic_number | MIT | [
"agentic_trivial",
"np_search"
] | An undirected simple graph has 15 vertices labelled 0..14 and edge list
[[1, 12], [2, 9], [2, 13], [3, 8], [3, 13], [4, 13], [5, 10], [7, 9], [7, 13], [8, 10]]
A harmonious colouring assigns colours so that (1) adjacent vertices get different colours and (2) for every unordered pair of distinct colours {x, y} there is... | {"n": 15, "k": 5, "edges": [[1, 12], [2, 9], [2, 13], [3, 8], [3, 13], [4, 13], [5, 10], [7, 9], [7, 13], [8, 10]], "family": "rlve_min_harmonious_coloring", "subset": "construct"} | null | null | null | {"colors": [0, 0, 0, 1, 2, 0, 0, 3, 2, 1, 3, 0, 2, 4, 0]} | 1 |
construct-rlve-min-harmonious-coloring-l5-s6 | construct | rlve_min_harmonious_coloring | harmonious_chromatic_number | graph_theory | competition | 5 | RLVE-Gym/minimum_harmonious_chromatic_number | MIT | [
"agentic_trivial",
"np_search"
] | An undirected simple graph has 15 vertices labelled 0..14 and edge list
[[0, 13], [1, 3], [1, 7], [1, 8], [1, 9], [1, 11], [2, 12], [2, 14], [3, 5], [3, 8], [4, 12], [6, 11], [8, 10], [9, 14], [13, 14]]
A harmonious colouring assigns colours so that (1) adjacent vertices get different colours and (2) for every unorder... | {"n": 15, "k": 6, "edges": [[0, 13], [1, 3], [1, 7], [1, 8], [1, 9], [1, 11], [2, 12], [2, 14], [3, 5], [3, 8], [4, 12], [6, 11], [8, 10], [9, 14], [13, 14]], "family": "rlve_min_harmonious_coloring", "subset": "construct"} | null | null | null | {"colors": [0, 1, 0, 2, 2, 0, 2, 0, 3, 4, 4, 5, 4, 3, 5]} | 1 |
construct-rlve-min-harmonious-coloring-l5-s7 | construct | rlve_min_harmonious_coloring | harmonious_chromatic_number | graph_theory | competition | 5 | RLVE-Gym/minimum_harmonious_chromatic_number | MIT | [
"agentic_trivial",
"np_search"
] | An undirected simple graph has 15 vertices labelled 0..14 and edge list
[[0, 5], [0, 6], [0, 8], [0, 9], [0, 12], [1, 4], [1, 7], [1, 10], [1, 13], [1, 14], [2, 12], [2, 14], [3, 8], [4, 9], [5, 9], [8, 9], [9, 12], [9, 14], [11, 12], [11, 14], [12, 13]]
A harmonious colouring assigns colours so that (1) adjacent vert... | {"n": 15, "k": 8, "edges": [[0, 5], [0, 6], [0, 8], [0, 9], [0, 12], [1, 4], [1, 7], [1, 10], [1, 13], [1, 14], [2, 12], [2, 14], [3, 8], [4, 9], [5, 9], [8, 9], [9, 12], [9, 14], [11, 12], [11, 14], [12, 13]], "family": "rlve_min_harmonious_coloring", "subset": "construct"} | null | null | null | {"colors": [0, 1, 2, 1, 2, 3, 1, 4, 5, 4, 6, 5, 6, 3, 7]} | 1 |
construct-rlve-min-harmonious-coloring-l5-s8 | construct | rlve_min_harmonious_coloring | harmonious_chromatic_number | graph_theory | competition | 5 | RLVE-Gym/minimum_harmonious_chromatic_number | MIT | [
"agentic_trivial",
"np_search"
] | An undirected simple graph has 15 vertices labelled 0..14 and edge list
[[0, 3], [0, 5], [0, 9], [0, 10], [1, 2], [1, 5], [1, 9], [1, 11], [1, 14], [2, 4], [3, 6], [6, 9], [6, 12], [8, 12], [9, 14]]
A harmonious colouring assigns colours so that (1) adjacent vertices get different colours and (2) for every unordered p... | {"n": 15, "k": 6, "edges": [[0, 3], [0, 5], [0, 9], [0, 10], [1, 2], [1, 5], [1, 9], [1, 11], [1, 14], [2, 4], [3, 6], [6, 9], [6, 12], [8, 12], [9, 14]], "family": "rlve_min_harmonious_coloring", "subset": "construct"} | null | null | null | {"colors": [0, 1, 2, 2, 3, 4, 4, 0, 2, 3, 5, 0, 5, 0, 5]} | 1 |
construct-rlve-min-harmonious-coloring-l5-s9 | construct | rlve_min_harmonious_coloring | harmonious_chromatic_number | graph_theory | competition | 5 | RLVE-Gym/minimum_harmonious_chromatic_number | MIT | [
"agentic_trivial",
"np_search"
] | An undirected simple graph has 15 vertices labelled 0..14 and edge list
[[0, 10], [0, 11], [0, 12], [1, 6], [1, 10], [1, 13], [2, 10], [2, 12], [3, 6], [3, 7], [3, 9], [3, 12], [4, 6], [4, 13], [5, 10], [5, 11], [5, 12], [5, 14], [6, 7], [8, 10], [8, 11], [9, 14], [10, 12], [10, 13], [10, 14], [11, 13]]
A harmonious c... | {"n": 15, "k": 9, "edges": [[0, 10], [0, 11], [0, 12], [1, 6], [1, 10], [1, 13], [2, 10], [2, 12], [3, 6], [3, 7], [3, 9], [3, 12], [4, 6], [4, 13], [5, 10], [5, 11], [5, 12], [5, 14], [6, 7], [8, 10], [8, 11], [9, 14], [10, 12], [10, 13], [10, 14], [11, 13]], "family": "rlve_min_harmonious_coloring", "subset": "constr... | null | null | null | {"colors": [0, 1, 2, 3, 0, 4, 4, 5, 3, 0, 6, 2, 7, 5, 8]} | 1 |
construct-rlve-min-harmonious-coloring-l6-s0 | construct | rlve_min_harmonious_coloring | harmonious_chromatic_number | graph_theory | competition | 6 | RLVE-Gym/minimum_harmonious_chromatic_number | MIT | [
"agentic_trivial",
"np_search"
] | An undirected simple graph has 18 vertices labelled 0..17 and edge list
[[0, 5], [0, 9], [0, 10], [0, 16], [1, 3], [1, 4], [1, 10], [1, 13], [1, 15], [2, 4], [2, 10], [2, 11], [3, 8], [3, 11], [3, 13], [3, 15], [3, 17], [4, 13], [5, 12], [5, 16], [5, 17], [6, 7], [6, 10], [6, 11], [6, 12], [6, 16], [7, 10], [7, 11], [7... | {"n": 18, "k": 13, "edges": [[0, 5], [0, 9], [0, 10], [0, 16], [1, 3], [1, 4], [1, 10], [1, 13], [1, 15], [2, 4], [2, 10], [2, 11], [3, 8], [3, 11], [3, 13], [3, 15], [3, 17], [4, 13], [5, 12], [5, 16], [5, 17], [6, 7], [6, 10], [6, 11], [6, 12], [6, 16], [7, 10], [7, 11], [7, 12], [7, 13], [7, 14], [8, 9], [8, 10], [8... | null | null | null | {"colors": [0, 1, 2, 0, 3, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 11, 12, 4]} | 1 |
construct-rlve-min-harmonious-coloring-l6-s1 | construct | rlve_min_harmonious_coloring | harmonious_chromatic_number | graph_theory | competition | 6 | RLVE-Gym/minimum_harmonious_chromatic_number | MIT | [
"agentic_trivial",
"np_search"
] | An undirected simple graph has 18 vertices labelled 0..17 and edge list
[[0, 1], [0, 5], [0, 9], [0, 10], [0, 12], [0, 14], [1, 8], [1, 13], [2, 3], [2, 13], [2, 17], [3, 6], [3, 8], [3, 10], [3, 11], [3, 13], [3, 14], [3, 17], [4, 6], [4, 8], [4, 11], [4, 14], [5, 7], [5, 9], [5, 12], [5, 13], [5, 14], [6, 13], [6, 17... | {"n": 18, "k": 13, "edges": [[0, 1], [0, 5], [0, 9], [0, 10], [0, 12], [0, 14], [1, 8], [1, 13], [2, 3], [2, 13], [2, 17], [3, 6], [3, 8], [3, 10], [3, 11], [3, 13], [3, 14], [3, 17], [4, 6], [4, 8], [4, 11], [4, 14], [5, 7], [5, 9], [5, 12], [5, 13], [5, 14], [6, 13], [6, 17], [8, 11], [9, 11], [9, 12], [9, 13], [10, ... | null | null | null | {"colors": [0, 1, 0, 2, 3, 4, 5, 1, 6, 7, 3, 8, 6, 9, 10, 1, 11, 12]} | 1 |
construct-rlve-min-harmonious-coloring-l6-s2 | construct | rlve_min_harmonious_coloring | harmonious_chromatic_number | graph_theory | competition | 6 | RLVE-Gym/minimum_harmonious_chromatic_number | MIT | [
"agentic_trivial",
"np_search"
] | An undirected simple graph has 18 vertices labelled 0..17 and edge list
[[0, 2], [0, 7], [0, 9], [0, 12], [0, 17], [1, 2], [1, 12], [1, 13], [2, 4], [2, 11], [2, 13], [2, 17], [3, 8], [3, 10], [3, 13], [3, 16], [3, 17], [4, 11], [5, 6], [5, 7], [5, 9], [5, 12], [5, 13], [5, 14], [5, 17], [6, 8], [6, 15], [6, 16], [7, 1... | {"n": 18, "k": 13, "edges": [[0, 2], [0, 7], [0, 9], [0, 12], [0, 17], [1, 2], [1, 12], [1, 13], [2, 4], [2, 11], [2, 13], [2, 17], [3, 8], [3, 10], [3, 13], [3, 16], [3, 17], [4, 11], [5, 6], [5, 7], [5, 9], [5, 12], [5, 13], [5, 14], [5, 17], [6, 8], [6, 15], [6, 16], [7, 10], [7, 13], [7, 16], [8, 10], [8, 12], [8, ... | null | null | null | {"colors": [0, 1, 2, 3, 3, 4, 0, 5, 6, 7, 1, 8, 9, 10, 2, 10, 11, 12]} | 1 |
construct-rlve-min-harmonious-coloring-l6-s3 | construct | rlve_min_harmonious_coloring | harmonious_chromatic_number | graph_theory | competition | 6 | RLVE-Gym/minimum_harmonious_chromatic_number | MIT | [
"agentic_trivial",
"np_search"
] | An undirected simple graph has 18 vertices labelled 0..17 and edge list
[[0, 15], [1, 3], [1, 5], [1, 7], [2, 10], [2, 13], [2, 15], [2, 16], [3, 9], [3, 10], [4, 6], [4, 11], [4, 13], [4, 15], [5, 7], [5, 11], [6, 17], [7, 13], [8, 11], [8, 12], [8, 13], [8, 15], [8, 17], [9, 11], [9, 15], [11, 14], [13, 17], [14, 15]... | {"n": 18, "k": 9, "edges": [[0, 15], [1, 3], [1, 5], [1, 7], [2, 10], [2, 13], [2, 15], [2, 16], [3, 9], [3, 10], [4, 6], [4, 11], [4, 13], [4, 15], [5, 7], [5, 11], [6, 17], [7, 13], [8, 11], [8, 12], [8, 13], [8, 15], [8, 17], [9, 11], [9, 15], [11, 14], [13, 17], [14, 15], [15, 17], [16, 17]], "family": "rlve_min_ha... | null | null | null | {"colors": [0, 1, 1, 0, 2, 3, 0, 4, 5, 4, 5, 6, 2, 7, 7, 8, 2, 3]} | 1 |
construct-rlve-min-harmonious-coloring-l6-s4 | construct | rlve_min_harmonious_coloring | harmonious_chromatic_number | graph_theory | competition | 6 | RLVE-Gym/minimum_harmonious_chromatic_number | MIT | [
"agentic_trivial",
"np_search"
] | An undirected simple graph has 18 vertices labelled 0..17 and edge list
[[0, 2], [0, 4], [0, 5], [0, 9], [1, 3], [1, 4], [1, 5], [1, 8], [1, 11], [2, 3], [2, 4], [2, 6], [2, 8], [2, 14], [2, 15], [3, 7], [3, 8], [3, 12], [4, 5], [4, 12], [4, 13], [4, 16], [5, 6], [5, 13], [5, 14], [5, 16], [5, 17], [6, 8], [6, 11], [6,... | {"n": 18, "k": 12, "edges": [[0, 2], [0, 4], [0, 5], [0, 9], [1, 3], [1, 4], [1, 5], [1, 8], [1, 11], [2, 3], [2, 4], [2, 6], [2, 8], [2, 14], [2, 15], [3, 7], [3, 8], [3, 12], [4, 5], [4, 12], [4, 13], [4, 16], [5, 6], [5, 13], [5, 14], [5, 16], [5, 17], [6, 8], [6, 11], [6, 12], [6, 17], [7, 10], [7, 14], [7, 17], [9... | null | null | null | {"colors": [0, 1, 2, 3, 4, 5, 6, 0, 7, 1, 8, 9, 10, 3, 9, 1, 7, 11]} | 1 |
construct-rlve-min-harmonious-coloring-l6-s5 | construct | rlve_min_harmonious_coloring | harmonious_chromatic_number | graph_theory | competition | 6 | RLVE-Gym/minimum_harmonious_chromatic_number | MIT | [
"agentic_trivial",
"np_search"
] | An undirected simple graph has 18 vertices labelled 0..17 and edge list
[[0, 4], [0, 6], [0, 10], [0, 16], [1, 3], [1, 5], [1, 13], [1, 14], [1, 17], [2, 11], [3, 16], [4, 16], [5, 11], [6, 11], [7, 9], [7, 10], [8, 11], [8, 16], [9, 11], [10, 14], [13, 14], [14, 17]]
A harmonious colouring assigns colours so that (1)... | {"n": 18, "k": 8, "edges": [[0, 4], [0, 6], [0, 10], [0, 16], [1, 3], [1, 5], [1, 13], [1, 14], [1, 17], [2, 11], [3, 16], [4, 16], [5, 11], [6, 11], [7, 9], [7, 10], [8, 11], [8, 16], [9, 11], [10, 14], [13, 14], [14, 17]], "family": "rlve_min_harmonious_coloring", "subset": "construct"} | null | null | null | {"colors": [0, 1, 0, 2, 1, 3, 4, 4, 5, 6, 3, 2, 0, 4, 5, 0, 7, 6]} | 1 |
construct-rlve-min-harmonious-coloring-l6-s6 | construct | rlve_min_harmonious_coloring | harmonious_chromatic_number | graph_theory | competition | 6 | RLVE-Gym/minimum_harmonious_chromatic_number | MIT | [
"agentic_trivial",
"np_search"
] | An undirected simple graph has 18 vertices labelled 0..17 and edge list
[[0, 1], [0, 9], [0, 12], [1, 4], [1, 12], [1, 13], [2, 8], [2, 11], [3, 9], [4, 8], [4, 12], [5, 6], [5, 10], [5, 12], [5, 14], [5, 16], [6, 9], [7, 8], [7, 10], [7, 14], [9, 10], [9, 14], [9, 15], [10, 11], [10, 12], [10, 15], [10, 16], [11, 13],... | {"n": 18, "k": 10, "edges": [[0, 1], [0, 9], [0, 12], [1, 4], [1, 12], [1, 13], [2, 8], [2, 11], [3, 9], [4, 8], [4, 12], [5, 6], [5, 10], [5, 12], [5, 14], [5, 16], [6, 9], [7, 8], [7, 10], [7, 14], [9, 10], [9, 14], [9, 15], [10, 11], [10, 12], [10, 15], [10, 16], [11, 13], [12, 16], [13, 15]], "family": "rlve_min_ha... | null | null | null | {"colors": [0, 1, 0, 1, 2, 3, 2, 1, 4, 5, 6, 2, 7, 8, 9, 4, 8, 0]} | 1 |
construct-rlve-min-harmonious-coloring-l6-s7 | construct | rlve_min_harmonious_coloring | harmonious_chromatic_number | graph_theory | competition | 6 | RLVE-Gym/minimum_harmonious_chromatic_number | MIT | [
"agentic_trivial",
"np_search"
] | An undirected simple graph has 18 vertices labelled 0..17 and edge list
[[0, 5], [0, 10], [0, 13], [0, 14], [1, 4], [1, 13], [2, 4], [2, 7], [2, 10], [3, 7], [3, 10], [4, 9], [4, 11], [5, 14], [5, 17], [6, 13], [6, 15], [7, 8], [7, 9], [7, 10], [8, 11], [9, 10], [9, 13], [9, 15], [10, 14], [11, 12], [11, 15], [14, 17],... | {"n": 18, "k": 9, "edges": [[0, 5], [0, 10], [0, 13], [0, 14], [1, 4], [1, 13], [2, 4], [2, 7], [2, 10], [3, 7], [3, 10], [4, 9], [4, 11], [5, 14], [5, 17], [6, 13], [6, 15], [7, 8], [7, 9], [7, 10], [8, 11], [9, 10], [9, 13], [9, 15], [10, 14], [11, 12], [11, 15], [14, 17], [15, 17], [16, 17]], "family": "rlve_min_har... | null | null | null | {"colors": [0, 1, 2, 1, 3, 4, 5, 6, 7, 4, 8, 0, 6, 2, 5, 1, 2, 7]} | 1 |
construct-rlve-min-harmonious-coloring-l6-s8 | construct | rlve_min_harmonious_coloring | harmonious_chromatic_number | graph_theory | competition | 6 | RLVE-Gym/minimum_harmonious_chromatic_number | MIT | [
"agentic_trivial",
"np_search"
] | An undirected simple graph has 18 vertices labelled 0..17 and edge list
[[0, 3], [0, 7], [0, 9], [1, 6], [1, 10], [1, 13], [2, 4], [2, 5], [3, 6], [3, 7], [3, 15], [4, 12], [4, 13], [4, 14], [5, 11], [6, 9], [6, 13], [6, 15], [7, 15], [7, 16], [8, 17], [9, 17], [10, 11], [10, 14], [10, 15], [11, 14], [12, 13], [12, 16]... | {"n": 18, "k": 9, "edges": [[0, 3], [0, 7], [0, 9], [1, 6], [1, 10], [1, 13], [2, 4], [2, 5], [3, 6], [3, 7], [3, 15], [4, 12], [4, 13], [4, 14], [5, 11], [6, 9], [6, 13], [6, 15], [7, 15], [7, 16], [8, 17], [9, 17], [10, 11], [10, 14], [10, 15], [11, 14], [12, 13], [12, 16], [13, 16], [15, 16]], "family": "rlve_min_ha... | null | null | null | {"colors": [0, 0, 0, 1, 2, 3, 4, 5, 1, 6, 7, 8, 1, 8, 5, 3, 6, 7]} | 1 |
construct-rlve-min-harmonious-coloring-l6-s9 | construct | rlve_min_harmonious_coloring | harmonious_chromatic_number | graph_theory | competition | 6 | RLVE-Gym/minimum_harmonious_chromatic_number | MIT | [
"agentic_trivial",
"np_search"
] | An undirected simple graph has 18 vertices labelled 0..17 and edge list
[[0, 2], [0, 5], [0, 6], [0, 12], [3, 9], [3, 10], [3, 11], [4, 14], [5, 14], [6, 11], [7, 10], [8, 17], [9, 10], [9, 12], [9, 14], [9, 15], [10, 11], [10, 13], [10, 15], [11, 13], [14, 17], [15, 17]]
A harmonious colouring assigns colours so that... | {"n": 18, "k": 8, "edges": [[0, 2], [0, 5], [0, 6], [0, 12], [3, 9], [3, 10], [3, 11], [4, 14], [5, 14], [6, 11], [7, 10], [8, 17], [9, 10], [9, 12], [9, 14], [9, 15], [10, 11], [10, 13], [10, 15], [11, 13], [14, 17], [15, 17]], "family": "rlve_min_harmonious_coloring", "subset": "construct"} | null | null | null | {"colors": [0, 0, 1, 0, 1, 2, 3, 1, 1, 4, 5, 6, 7, 7, 3, 2, 0, 7]} | 1 |
construct-rlve-pairwise-sums-recovery-l1-s0 | construct | rlve_pairwise_sums_recovery | poi_squarks_pairwise_sums | combinatorics | competition | 1 | RLVE-Gym/squ_squarks | MIT | [
"agentic_trivial"
] | Find 3 distinct positive integers whose 3 pairwise sums (over all unordered pairs), taken as a multiset, are exactly:
9, 8, 7
Answer format: {"numbers": [x_1, ..., x_3]}
Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is gra... | {"n": 3, "sums": [9, 8, 7], "family": "rlve_pairwise_sums_recovery", "subset": "construct"} | null | null | null | {"numbers": [3, 4, 5]} | 1 |
construct-rlve-pairwise-sums-recovery-l1-s1 | construct | rlve_pairwise_sums_recovery | poi_squarks_pairwise_sums | combinatorics | competition | 1 | RLVE-Gym/squ_squarks | MIT | [
"agentic_trivial"
] | Find 3 distinct positive integers whose 3 pairwise sums (over all unordered pairs), taken as a multiset, are exactly:
5, 7, 4
Answer format: {"numbers": [x_1, ..., x_3]}
Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is gra... | {"n": 3, "sums": [5, 7, 4], "family": "rlve_pairwise_sums_recovery", "subset": "construct"} | null | null | null | {"numbers": [1, 3, 4]} | 1 |
construct-rlve-pairwise-sums-recovery-l1-s2 | construct | rlve_pairwise_sums_recovery | poi_squarks_pairwise_sums | combinatorics | competition | 1 | RLVE-Gym/squ_squarks | MIT | [
"agentic_trivial"
] | Find 3 distinct positive integers whose 3 pairwise sums (over all unordered pairs), taken as a multiset, are exactly:
4, 5, 7
Answer format: {"numbers": [x_1, ..., x_3]}
Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is gra... | {"n": 3, "sums": [4, 5, 7], "family": "rlve_pairwise_sums_recovery", "subset": "construct"} | null | null | null | {"numbers": [1, 3, 4]} | 1 |
construct-rlve-pairwise-sums-recovery-l1-s3 | construct | rlve_pairwise_sums_recovery | poi_squarks_pairwise_sums | combinatorics | competition | 1 | RLVE-Gym/squ_squarks | MIT | [
"agentic_trivial"
] | Find 3 distinct positive integers whose 3 pairwise sums (over all unordered pairs), taken as a multiset, are exactly:
9, 10, 11
Answer format: {"numbers": [x_1, ..., x_3]}
Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is g... | {"n": 3, "sums": [9, 10, 11], "family": "rlve_pairwise_sums_recovery", "subset": "construct"} | null | null | null | {"numbers": [4, 5, 6]} | 1 |
construct-rlve-pairwise-sums-recovery-l1-s4 | construct | rlve_pairwise_sums_recovery | poi_squarks_pairwise_sums | combinatorics | competition | 1 | RLVE-Gym/squ_squarks | MIT | [
"agentic_trivial"
] | Find 3 distinct positive integers whose 3 pairwise sums (over all unordered pairs), taken as a multiset, are exactly:
9, 5, 8
Answer format: {"numbers": [x_1, ..., x_3]}
Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is gra... | {"n": 3, "sums": [9, 5, 8], "family": "rlve_pairwise_sums_recovery", "subset": "construct"} | null | null | null | {"numbers": [2, 3, 6]} | 1 |
construct-rlve-pairwise-sums-recovery-l1-s5 | construct | rlve_pairwise_sums_recovery | poi_squarks_pairwise_sums | combinatorics | competition | 1 | RLVE-Gym/squ_squarks | MIT | [
"agentic_trivial"
] | Find 3 distinct positive integers whose 3 pairwise sums (over all unordered pairs), taken as a multiset, are exactly:
9, 4, 7
Answer format: {"numbers": [x_1, ..., x_3]}
Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is gra... | {"n": 3, "sums": [9, 4, 7], "family": "rlve_pairwise_sums_recovery", "subset": "construct"} | null | null | null | {"numbers": [1, 3, 6]} | 1 |
construct-rlve-pairwise-sums-recovery-l1-s6 | construct | rlve_pairwise_sums_recovery | poi_squarks_pairwise_sums | combinatorics | competition | 1 | RLVE-Gym/squ_squarks | MIT | [
"agentic_trivial"
] | Find 3 distinct positive integers whose 3 pairwise sums (over all unordered pairs), taken as a multiset, are exactly:
11, 8, 7
Answer format: {"numbers": [x_1, ..., x_3]}
Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is gr... | {"n": 3, "sums": [11, 8, 7], "family": "rlve_pairwise_sums_recovery", "subset": "construct"} | null | null | null | {"numbers": [2, 5, 6]} | 1 |
construct-rlve-pairwise-sums-recovery-l1-s7 | construct | rlve_pairwise_sums_recovery | poi_squarks_pairwise_sums | combinatorics | competition | 1 | RLVE-Gym/squ_squarks | MIT | [
"agentic_trivial"
] | Find 3 distinct positive integers whose 3 pairwise sums (over all unordered pairs), taken as a multiset, are exactly:
6, 7, 3
Answer format: {"numbers": [x_1, ..., x_3]}
Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is gra... | {"n": 3, "sums": [6, 7, 3], "family": "rlve_pairwise_sums_recovery", "subset": "construct"} | null | null | null | {"numbers": [1, 2, 5]} | 1 |
construct-rlve-pairwise-sums-recovery-l1-s8 | construct | rlve_pairwise_sums_recovery | poi_squarks_pairwise_sums | combinatorics | competition | 1 | RLVE-Gym/squ_squarks | MIT | [
"agentic_trivial"
] | Find 3 distinct positive integers whose 3 pairwise sums (over all unordered pairs), taken as a multiset, are exactly:
5, 6, 3
Answer format: {"numbers": [x_1, ..., x_3]}
Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is gra... | {"n": 3, "sums": [5, 6, 3], "family": "rlve_pairwise_sums_recovery", "subset": "construct"} | null | null | null | {"numbers": [1, 2, 4]} | 1 |
construct-rlve-pairwise-sums-recovery-l1-s9 | construct | rlve_pairwise_sums_recovery | poi_squarks_pairwise_sums | combinatorics | competition | 1 | RLVE-Gym/squ_squarks | MIT | [
"agentic_trivial"
] | Find 3 distinct positive integers whose 3 pairwise sums (over all unordered pairs), taken as a multiset, are exactly:
6, 7, 5
Answer format: {"numbers": [x_1, ..., x_3]}
Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is gra... | {"n": 3, "sums": [6, 7, 5], "family": "rlve_pairwise_sums_recovery", "subset": "construct"} | null | null | null | {"numbers": [2, 3, 4]} | 1 |
construct-rlve-pairwise-sums-recovery-l2-s0 | construct | rlve_pairwise_sums_recovery | poi_squarks_pairwise_sums | combinatorics | competition | 2 | RLVE-Gym/squ_squarks | MIT | [
"agentic_trivial"
] | Find 5 distinct positive integers whose 10 pairwise sums (over all unordered pairs), taken as a multiset, are exactly:
11, 8, 15, 13, 9, 7, 10, 8, 16, 3
Answer format: {"numbers": [x_1, ..., x_5]}
Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/... | {"n": 5, "sums": [11, 8, 15, 13, 9, 7, 10, 8, 16, 3], "family": "rlve_pairwise_sums_recovery", "subset": "construct"} | null | null | null | {"numbers": [1, 2, 6, 7, 9]} | 1 |
construct-rlve-pairwise-sums-recovery-l2-s1 | construct | rlve_pairwise_sums_recovery | poi_squarks_pairwise_sums | combinatorics | competition | 2 | RLVE-Gym/squ_squarks | MIT | [
"agentic_trivial"
] | Find 5 distinct positive integers whose 10 pairwise sums (over all unordered pairs), taken as a multiset, are exactly:
5, 12, 11, 6, 9, 7, 7, 8, 9, 10
Answer format: {"numbers": [x_1, ..., x_5]}
Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/wo... | {"n": 5, "sums": [5, 12, 11, 6, 9, 7, 7, 8, 9, 10], "family": "rlve_pairwise_sums_recovery", "subset": "construct"} | null | null | null | {"numbers": [2, 3, 4, 5, 7]} | 1 |
construct-rlve-pairwise-sums-recovery-l2-s2 | construct | rlve_pairwise_sums_recovery | poi_squarks_pairwise_sums | combinatorics | competition | 2 | RLVE-Gym/squ_squarks | MIT | [
"agentic_trivial"
] | Find 5 distinct positive integers whose 10 pairwise sums (over all unordered pairs), taken as a multiset, are exactly:
9, 12, 3, 8, 6, 11, 5, 9, 6, 7
Answer format: {"numbers": [x_1, ..., x_5]}
Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/wor... | {"n": 5, "sums": [9, 12, 3, 8, 6, 11, 5, 9, 6, 7], "family": "rlve_pairwise_sums_recovery", "subset": "construct"} | null | null | null | {"numbers": [1, 2, 4, 5, 7]} | 1 |
construct-rlve-pairwise-sums-recovery-l2-s3 | construct | rlve_pairwise_sums_recovery | poi_squarks_pairwise_sums | combinatorics | competition | 2 | RLVE-Gym/squ_squarks | MIT | [
"agentic_trivial"
] | Find 5 distinct positive integers whose 10 pairwise sums (over all unordered pairs), taken as a multiset, are exactly:
15, 12, 13, 8, 9, 12, 11, 10, 7, 11
Answer format: {"numbers": [x_1, ..., x_5]}
Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only ... | {"n": 5, "sums": [15, 12, 13, 8, 9, 12, 11, 10, 7, 11], "family": "rlve_pairwise_sums_recovery", "subset": "construct"} | null | null | null | {"numbers": [3, 4, 5, 7, 8]} | 1 |
construct-rlve-pairwise-sums-recovery-l2-s4 | construct | rlve_pairwise_sums_recovery | poi_squarks_pairwise_sums | combinatorics | competition | 2 | RLVE-Gym/squ_squarks | MIT | [
"agentic_trivial"
] | Find 5 distinct positive integers whose 10 pairwise sums (over all unordered pairs), taken as a multiset, are exactly:
7, 10, 13, 17, 8, 15, 12, 5, 9, 12
Answer format: {"numbers": [x_1, ..., x_5]}
Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `... | {"n": 5, "sums": [7, 10, 13, 17, 8, 15, 12, 5, 9, 12], "family": "rlve_pairwise_sums_recovery", "subset": "construct"} | null | null | null | {"numbers": [2, 3, 5, 7, 10]} | 1 |
construct-rlve-pairwise-sums-recovery-l2-s5 | construct | rlve_pairwise_sums_recovery | poi_squarks_pairwise_sums | combinatorics | competition | 2 | RLVE-Gym/squ_squarks | MIT | [
"agentic_trivial"
] | Find 5 distinct positive integers whose 10 pairwise sums (over all unordered pairs), taken as a multiset, are exactly:
12, 9, 15, 13, 10, 16, 19, 13, 16, 17
Answer format: {"numbers": [x_1, ..., x_5]}
Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Onl... | {"n": 5, "sums": [12, 9, 15, 13, 10, 16, 19, 13, 16, 17], "family": "rlve_pairwise_sums_recovery", "subset": "construct"} | null | null | null | {"numbers": [3, 6, 7, 9, 10]} | 1 |
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