name stringlengths 14 134 | problem_type stringclasses 25
values | params dict | prompt stringlengths 167 1k | satisfiable bool 2
classes | solution dict | difficulty dict | partial_assignment dict |
|---|---|---|---|---|---|---|---|
pysms_clique_coloring_max_chromatic_number4_max_clique2_min_degree1_vertices15__v7_h | pysms_clique_coloring | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": 4,
"min_edges": null,
"min_girth": null,
"vertices": 15,
"max_clique": 2,
"min_degree": 1,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic_numbe... | Generate a graph with 15 vertices where the maximum clique size is at most 2, the chromatic number is at most 4, and every vertex has degree at least 1.
Return the graph as a list of edges (u, v) with 0 <= u < v < 15, or state "UNSATISFIABLE" if no graph exists.
Partial assignment (fixed values that must be respected... | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
2
],
[
0,
3
],
[
0,
4
],
[
0,
5
],
[
0,
6
],
[
0,
7
],
[
0,
8
],
[
0,
9
],
[
... | {
"solve_time_ms": 94.8,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 26,
"backend": "pysms",
"solve_tier": "medium",
"solve_pct_global": 36.28,
"solve_pct_type": 70.83
} | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
1,
8
],
[
1,
9
],
[
0,
10
],
[
0,
6
],
[
0,
5
]
],
"q": null
} |
pysms_clique_coloring_max_chromatic_number4_max_clique3_min_degree1_vertices16__v10_h | pysms_clique_coloring | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": 4,
"min_edges": null,
"min_girth": null,
"vertices": 16,
"max_clique": 3,
"min_degree": 1,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic_numbe... | Generate a graph with 16 vertices where the maximum clique size is at most 3, the chromatic number is at most 4, and every vertex has degree at least 1.
Return the graph as a list of edges (u, v) with 0 <= u < v < 16, or state "UNSATISFIABLE" if no graph exists.
Partial assignment (fixed values that must be respected... | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
2
],
[
0,
3
],
[
0,
4
],
[
0,
5
],
[
0,
6
],
[
0,
7
],
[
0,
8
],
[
0,
9
],
[
... | {
"solve_time_ms": 97.8,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 28,
"backend": "pysms",
"solve_tier": "medium",
"solve_pct_global": 38.91,
"solve_pct_type": 87.5
} | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
1,
7
],
[
1,
10
],
[
0,
8
],
[
0,
3
],
[
1,
14
]
],
"q": null
} |
pysms_clique_coloring_max_chromatic_number4_max_clique5_min_degree4_vertices11__v9_nh | pysms_clique_coloring | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": 4,
"min_edges": null,
"min_girth": null,
"vertices": 11,
"max_clique": 5,
"min_degree": 4,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic_numbe... | Generate a graph with 11 vertices where the maximum clique size is at most 5, the chromatic number is at most 4, and every vertex has degree at least 4.
Return the graph as a list of edges (u, v) with 0 <= u < v < 11, or state "UNSATISFIABLE" if no graph exists. | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
5
],
[
0,
6
],
[
0,
7
],
[
0,
8
],
[
0,
9
],
[
0,
10
],
[
1,
3
],
[
1,
4
],
[
... | {
"solve_time_ms": 25.2,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 40,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 14.47,
"solve_pct_type": 12.5
} | null |
pysms_clique_coloring_max_chromatic_number5_max_clique2_min_degree3_vertices15__v11_nh | pysms_clique_coloring | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": 5,
"min_edges": null,
"min_girth": null,
"vertices": 15,
"max_clique": 2,
"min_degree": 3,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic_numbe... | Generate a graph with 15 vertices where the maximum clique size is at most 2, the chromatic number is at most 5, and every vertex has degree at least 3.
Return the graph as a list of edges (u, v) with 0 <= u < v < 15, or state "UNSATISFIABLE" if no graph exists. | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
3
],
[
0,
4
],
[
0,
5
],
[
0,
6
],
[
0,
7
],
[
0,
8
],
[
0,
9
],
[
0,
10
],
[
... | {
"solve_time_ms": 93.6,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 36,
"backend": "pysms",
"solve_tier": "medium",
"solve_pct_global": 34.02,
"solve_pct_type": 54.17
} | null |
pysms_clique_coloring_max_chromatic_number5_max_clique4_min_degree1_vertices14__v5_h | pysms_clique_coloring | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": 5,
"min_edges": null,
"min_girth": null,
"vertices": 14,
"max_clique": 4,
"min_degree": 1,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic_numbe... | Generate a graph with 14 vertices where the maximum clique size is at most 4, the chromatic number is at most 5, and every vertex has degree at least 1.
Return the graph as a list of edges (u, v) with 0 <= u < v < 14, or state "UNSATISFIABLE" if no graph exists.
Partial assignment (fixed values that must be respected... | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
2
],
[
0,
3
],
[
0,
4
],
[
0,
5
],
[
0,
6
],
[
0,
7
],
[
0,
8
],
[
0,
9
],
[
... | {
"solve_time_ms": 93.9,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 24,
"backend": "pysms",
"solve_tier": "medium",
"solve_pct_global": 34.4,
"solve_pct_type": 62.5
} | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
1,
4
],
[
1,
2
],
[
1,
9
],
[
0,
3
]
],
"q": null
} |
pysms_clique_coloring_max_chromatic_number5_max_clique4_min_degree4_vertices12__v0_h | pysms_clique_coloring | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": 5,
"min_edges": null,
"min_girth": null,
"vertices": 12,
"max_clique": 4,
"min_degree": 4,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic_numbe... | Generate a graph with 12 vertices where the maximum clique size is at most 4, the chromatic number is at most 5, and every vertex has degree at least 4.
Return the graph as a list of edges (u, v) with 0 <= u < v < 12, or state "UNSATISFIABLE" if no graph exists.
Partial assignment (fixed values that must be respected... | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
3
],
[
0,
4
],
[
0,
5
],
[
0,
6
],
[
0,
7
],
[
0,
8
],
[
0,
9
],
[
0,
10
],
[
... | {
"solve_time_ms": 184.3,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 35,
"backend": "pysms",
"solve_tier": "medium",
"solve_pct_global": 48.68,
"solve_pct_type": 95.83
} | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
10
],
[
0,
11
],
[
0,
7
],
[
3,
10
],
[
2,
9
],
[
1,
9
],
[
3,
6
]
],
"q": null
} |
pysms_clique_coloring_max_chromatic_number5_max_clique5_min_degree4_vertices13__v4_h | pysms_clique_coloring | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": 5,
"min_edges": null,
"min_girth": null,
"vertices": 13,
"max_clique": 5,
"min_degree": 4,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic_numbe... | Generate a graph with 13 vertices where the maximum clique size is at most 5, the chromatic number is at most 5, and every vertex has degree at least 4.
Return the graph as a list of edges (u, v) with 0 <= u < v < 13, or state "UNSATISFIABLE" if no graph exists.
Partial assignment (fixed values that must be respected... | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
1
],
[
0,
2
],
[
0,
3
],
[
0,
4
],
[
0,
5
],
[
0,
6
],
[
0,
7
],
[
0,
8
],
[
... | {
"solve_time_ms": 92,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 42,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 33.27,
"solve_pct_type": 45.83
} | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
1,
3
],
[
2,
7
],
[
3,
11
],
[
3,
10
],
[
0,
12
],
[
2,
10
],
[
2,
4
],
[
1,
11
]
],
... |
pysms_combined_graph_h0e5a7a55d5dd__v3 | pysms_combined_graph | {
"n": null,
"k": 3,
"p": null,
"max_chromatic_number": 2,
"min_edges": 16,
"min_girth": 5,
"vertices": 13,
"max_clique": 4,
"min_degree": 1,
"clique_size": 4,
"max_degree": 4,
"max_edges": 19,
"max_independent_set": 3,
"maximal_triangle_free": false,
"min_chromatic_number": 2,
"min_conn... | Generate a graph with 13 vertices that satisfies: minimum degree >= 1, maximum degree <= 4, edges between 16 and 19, maximum clique size <= 4, maximum independent set size <= 3, chromatic number <= 2, chromatic number >= 2, vertex-connectivity >= 1, girth >= 5, C_3-free, consists of exactly 2 vertex-disjoint cliques of... | false | null | {
"solve_time_ms": 21.5,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": -1,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 12.22,
"solve_pct_type": 12.5
} | null |
pysms_combined_graph_h2eb2bb78ad1f__v1 | pysms_combined_graph | {
"n": null,
"k": 4,
"p": null,
"max_chromatic_number": 4,
"min_edges": 12,
"min_girth": 5,
"vertices": 12,
"max_clique": 4,
"min_degree": 2,
"clique_size": 3,
"max_degree": 5,
"max_edges": 18,
"max_independent_set": 3,
"maximal_triangle_free": false,
"min_chromatic_number": 3,
"min_conn... | Generate a graph with 12 vertices that satisfies: minimum degree >= 2, maximum degree <= 5, edges between 12 and 18, maximum clique size <= 4, maximum independent set size <= 3, chromatic number <= 4, chromatic number >= 3, vertex-connectivity >= 2, girth >= 5, C_4-free, consists of exactly 2 vertex-disjoint cliques of... | false | null | {
"solve_time_ms": 45,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": -1,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 20.49,
"solve_pct_type": 62.5
} | null |
pysms_combined_graph_h32c81275d5e7__v0 | pysms_combined_graph | {
"n": null,
"k": 4,
"p": null,
"max_chromatic_number": 4,
"min_edges": 22,
"min_girth": 4,
"vertices": 12,
"max_clique": 4,
"min_degree": 3,
"clique_size": 3,
"max_degree": 4,
"max_edges": 16,
"max_independent_set": 5,
"maximal_triangle_free": false,
"min_chromatic_number": 3,
"min_conn... | Generate a graph with 12 vertices that satisfies: minimum degree >= 3, maximum degree <= 4, edges between 22 and 16, maximum clique size <= 4, maximum independent set size <= 5, chromatic number <= 4, chromatic number >= 3, vertex-connectivity >= 2, girth >= 4, C_4-free, consists of exactly 2 vertex-disjoint cliques of... | false | null | {
"solve_time_ms": 46,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": -1,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 20.86,
"solve_pct_type": 70.83
} | null |
pysms_combined_graph_h5e56d1e3f16b__v4 | pysms_combined_graph | {
"n": null,
"k": 4,
"p": null,
"max_chromatic_number": 2,
"min_edges": 24,
"min_girth": 5,
"vertices": 11,
"max_clique": 4,
"min_degree": 2,
"clique_size": 3,
"max_degree": 4,
"max_edges": 19,
"max_independent_set": 2,
"maximal_triangle_free": false,
"min_chromatic_number": 2,
"min_conn... | Generate a graph with 11 vertices that satisfies: minimum degree >= 2, maximum degree <= 4, edges between 24 and 19, maximum clique size <= 4, maximum independent set size <= 2, chromatic number <= 2, chromatic number >= 2, vertex-connectivity >= 2, girth >= 5, C_4-free, consists of exactly 2 vertex-disjoint cliques of... | false | null | {
"solve_time_ms": 33.8,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": -1,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 18.61,
"solve_pct_type": 45.83
} | null |
pysms_combined_graph_h608ef60f8b6f__v11 | pysms_combined_graph | {
"n": null,
"k": 3,
"p": null,
"max_chromatic_number": 3,
"min_edges": 12,
"min_girth": 3,
"vertices": 15,
"max_clique": 3,
"min_degree": 1,
"clique_size": 3,
"max_degree": 3,
"max_edges": 22,
"max_independent_set": 5,
"maximal_triangle_free": false,
"min_chromatic_number": 2,
"min_conn... | Generate a graph with 15 vertices that satisfies: minimum degree >= 1, maximum degree <= 3, edges between 12 and 22, maximum clique size <= 3, maximum independent set size <= 5, chromatic number <= 3, chromatic number >= 2, vertex-connectivity >= 2, girth >= 3, C_3-free, consists of exactly 2 vertex-disjoint cliques of... | false | null | {
"solve_time_ms": 98.9,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": -1,
"backend": "pysms",
"solve_tier": "medium",
"solve_pct_global": 40.04,
"solve_pct_type": 95.83
} | null |
pysms_combined_graph_h84c3e3bbf340__v9 | pysms_combined_graph | {
"n": null,
"k": 4,
"p": null,
"max_chromatic_number": 4,
"min_edges": 13,
"min_girth": 4,
"vertices": 13,
"max_clique": 3,
"min_degree": 1,
"clique_size": 4,
"max_degree": 3,
"max_edges": 23,
"max_independent_set": 2,
"maximal_triangle_free": false,
"min_chromatic_number": 3,
"min_conn... | Generate a graph with 13 vertices that satisfies: minimum degree >= 1, maximum degree <= 3, edges between 13 and 23, maximum clique size <= 3, maximum independent set size <= 2, chromatic number <= 4, chromatic number >= 3, vertex-connectivity >= 2, girth >= 4, C_4-free, consists of exactly 1 vertex-disjoint cliques of... | false | null | {
"solve_time_ms": 54.9,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": -1,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 23.5,
"solve_pct_type": 79.17
} | null |
pysms_combined_graph_h85b189296554__v6 | pysms_combined_graph | {
"n": null,
"k": 3,
"p": null,
"max_chromatic_number": 3,
"min_edges": 21,
"min_girth": 4,
"vertices": 16,
"max_clique": 2,
"min_degree": 1,
"clique_size": 3,
"max_degree": 3,
"max_edges": 19,
"max_independent_set": 5,
"maximal_triangle_free": false,
"min_chromatic_number": 2,
"min_conn... | Generate a graph with 16 vertices that satisfies: minimum degree >= 1, maximum degree <= 3, edges between 21 and 19, maximum clique size <= 2, maximum independent set size <= 5, chromatic number <= 3, chromatic number >= 2, vertex-connectivity >= 1, girth >= 4, C_3-free, consists of exactly 1 vertex-disjoint cliques of... | false | null | {
"solve_time_ms": 32.5,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": -1,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 17.11,
"solve_pct_type": 37.5
} | null |
pysms_combined_graph_hac965a2fcbae__v10 | pysms_combined_graph | {
"n": null,
"k": 3,
"p": null,
"max_chromatic_number": 4,
"min_edges": 13,
"min_girth": 3,
"vertices": 15,
"max_clique": 2,
"min_degree": 3,
"clique_size": 3,
"max_degree": 4,
"max_edges": 21,
"max_independent_set": 5,
"maximal_triangle_free": false,
"min_chromatic_number": 2,
"min_conn... | Generate a graph with 15 vertices that satisfies: minimum degree >= 3, maximum degree <= 4, edges between 13 and 21, maximum clique size <= 2, maximum independent set size <= 5, chromatic number <= 4, chromatic number >= 2, vertex-connectivity >= 2, girth >= 3, C_3-free, consists of exactly 2 vertex-disjoint cliques of... | false | null | {
"solve_time_ms": 98.2,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": -1,
"backend": "pysms",
"solve_tier": "medium",
"solve_pct_global": 39.29,
"solve_pct_type": 87.5
} | null |
pysms_combined_graph_hbb56eb209162__v7 | pysms_combined_graph | {
"n": null,
"k": 3,
"p": null,
"max_chromatic_number": 4,
"min_edges": 10,
"min_girth": 5,
"vertices": 12,
"max_clique": 2,
"min_degree": 2,
"clique_size": 3,
"max_degree": 4,
"max_edges": 27,
"max_independent_set": 2,
"maximal_triangle_free": false,
"min_chromatic_number": 3,
"min_conn... | Generate a graph with 12 vertices that satisfies: minimum degree >= 2, maximum degree <= 4, edges between 10 and 27, maximum clique size <= 2, maximum independent set size <= 2, chromatic number <= 4, chromatic number >= 3, vertex-connectivity >= 1, girth >= 5, C_3-free, consists of exactly 2 vertex-disjoint cliques of... | false | null | {
"solve_time_ms": 17.1,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": -1,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 9.21,
"solve_pct_type": 4.17
} | null |
pysms_combined_graph_hefbad864c275__v2 | pysms_combined_graph | {
"n": null,
"k": 3,
"p": null,
"max_chromatic_number": 4,
"min_edges": 10,
"min_girth": 5,
"vertices": 10,
"max_clique": 4,
"min_degree": 3,
"clique_size": 4,
"max_degree": 5,
"max_edges": 28,
"max_independent_set": 3,
"maximal_triangle_free": false,
"min_chromatic_number": 3,
"min_conn... | Generate a graph with 10 vertices that satisfies: minimum degree >= 3, maximum degree <= 5, edges between 10 and 28, maximum clique size <= 4, maximum independent set size <= 3, chromatic number <= 4, chromatic number >= 3, vertex-connectivity >= 2, girth >= 5, C_3-free, consists of exactly 1 vertex-disjoint cliques of... | false | null | {
"solve_time_ms": 28.4,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": -1,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 15.41,
"solve_pct_type": 29.17
} | null |
pysms_combined_graph_hf0fd165af7c5__v8 | pysms_combined_graph | {
"n": null,
"k": 4,
"p": null,
"max_chromatic_number": 4,
"min_edges": 15,
"min_girth": 5,
"vertices": 10,
"max_clique": 3,
"min_degree": 1,
"clique_size": 4,
"max_degree": 4,
"max_edges": 18,
"max_independent_set": 2,
"maximal_triangle_free": false,
"min_chromatic_number": 3,
"min_conn... | Generate a graph with 10 vertices that satisfies: minimum degree >= 1, maximum degree <= 4, edges between 15 and 18, maximum clique size <= 3, maximum independent set size <= 2, chromatic number <= 4, chromatic number >= 3, vertex-connectivity >= 2, girth >= 5, C_4-free, consists of exactly 1 vertex-disjoint cliques of... | false | null | {
"solve_time_ms": 23.3,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": -1,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 13.72,
"solve_pct_type": 20.83
} | null |
pysms_combined_graph_hf81fee16a11b__v5 | pysms_combined_graph | {
"n": null,
"k": 3,
"p": null,
"max_chromatic_number": 2,
"min_edges": 18,
"min_girth": 3,
"vertices": 15,
"max_clique": 3,
"min_degree": 3,
"clique_size": 3,
"max_degree": 5,
"max_edges": 15,
"max_independent_set": 3,
"maximal_triangle_free": false,
"min_chromatic_number": 2,
"min_conn... | Generate a graph with 15 vertices that satisfies: minimum degree >= 3, maximum degree <= 5, edges between 18 and 15, maximum clique size <= 3, maximum independent set size <= 3, chromatic number <= 2, chromatic number >= 2, vertex-connectivity >= 1, girth >= 3, C_3-free, consists of exactly 2 vertex-disjoint cliques of... | false | null | {
"solve_time_ms": 35.3,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": -1,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 19.36,
"solve_pct_type": 54.17
} | null |
pysms_contains_cliques_clique_size3_num_cliques1_vertices10__v5 | pysms_contains_cliques | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": 10,
"max_clique": null,
"min_degree": null,
"clique_size": 3,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic... | Generate a graph with 10 vertices that consists of exactly 1 vertex-disjoint clique(s), each of size 3. Every vertex must belong to one of these cliques, and the only edges in the graph are those within these cliques.
Return the graph as a list of edges (u, v) with 0 <= u < v < 10, or state "UNSATISFIABLE" if no graph... | false | null | {
"solve_time_ms": 8.5,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": -1,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 1.13,
"solve_pct_type": 16.67
} | null |
pysms_contains_cliques_clique_size3_num_cliques1_vertices15__v0 | pysms_contains_cliques | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": 15,
"max_clique": null,
"min_degree": null,
"clique_size": 3,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic... | Generate a graph with 15 vertices that consists of exactly 1 vertex-disjoint clique(s), each of size 3. Every vertex must belong to one of these cliques, and the only edges in the graph are those within these cliques.
Return the graph as a list of edges (u, v) with 0 <= u < v < 15, or state "UNSATISFIABLE" if no graph... | false | null | {
"solve_time_ms": 8.9,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": -1,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 2.26,
"solve_pct_type": 41.67
} | null |
pysms_contains_cliques_clique_size3_num_cliques3_vertices14__v3 | pysms_contains_cliques | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": 14,
"max_clique": null,
"min_degree": null,
"clique_size": 3,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic... | Generate a graph with 14 vertices that consists of exactly 3 vertex-disjoint clique(s), each of size 3. Every vertex must belong to one of these cliques, and the only edges in the graph are those within these cliques.
Return the graph as a list of edges (u, v) with 0 <= u < v < 14, or state "UNSATISFIABLE" if no graph... | false | null | {
"solve_time_ms": 11.3,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": -1,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 6.2,
"solve_pct_type": 79.17
} | null |
pysms_contains_cliques_clique_size3_num_cliques3_vertices16__v6 | pysms_contains_cliques | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": 16,
"max_clique": null,
"min_degree": null,
"clique_size": 3,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic... | Generate a graph with 16 vertices that consists of exactly 3 vertex-disjoint clique(s), each of size 3. Every vertex must belong to one of these cliques, and the only edges in the graph are those within these cliques.
Return the graph as a list of edges (u, v) with 0 <= u < v < 16, or state "UNSATISFIABLE" if no graph... | false | null | {
"solve_time_ms": 11.7,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": -1,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 6.95,
"solve_pct_type": 87.5
} | null |
pysms_contains_cliques_clique_size3_num_cliques4_vertices16__v4 | pysms_contains_cliques | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": 16,
"max_clique": null,
"min_degree": null,
"clique_size": 3,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic... | Generate a graph with 16 vertices that consists of exactly 4 vertex-disjoint clique(s), each of size 3. Every vertex must belong to one of these cliques, and the only edges in the graph are those within these cliques.
Return the graph as a list of edges (u, v) with 0 <= u < v < 16, or state "UNSATISFIABLE" if no graph... | false | null | {
"solve_time_ms": 28.4,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": -1,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 15.41,
"solve_pct_type": 95.83
} | null |
pysms_contains_cliques_clique_size4_num_cliques1_vertices13__v8 | pysms_contains_cliques | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": 13,
"max_clique": null,
"min_degree": null,
"clique_size": 4,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic... | Generate a graph with 13 vertices that consists of exactly 1 vertex-disjoint clique(s), each of size 4. Every vertex must belong to one of these cliques, and the only edges in the graph are those within these cliques.
Return the graph as a list of edges (u, v) with 0 <= u < v < 13, or state "UNSATISFIABLE" if no graph... | false | null | {
"solve_time_ms": 8.6,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": -1,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 1.69,
"solve_pct_type": 29.17
} | null |
pysms_contains_cliques_clique_size4_num_cliques1_vertices14__v7 | pysms_contains_cliques | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": 14,
"max_clique": null,
"min_degree": null,
"clique_size": 4,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic... | Generate a graph with 14 vertices that consists of exactly 1 vertex-disjoint clique(s), each of size 4. Every vertex must belong to one of these cliques, and the only edges in the graph are those within these cliques.
Return the graph as a list of edges (u, v) with 0 <= u < v < 14, or state "UNSATISFIABLE" if no graph... | false | null | {
"solve_time_ms": 8.5,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": -1,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 1.13,
"solve_pct_type": 16.67
} | null |
pysms_contains_cliques_clique_size4_num_cliques2_vertices10__v10 | pysms_contains_cliques | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": 10,
"max_clique": null,
"min_degree": null,
"clique_size": 4,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic... | Generate a graph with 10 vertices that consists of exactly 2 vertex-disjoint clique(s), each of size 4. Every vertex must belong to one of these cliques, and the only edges in the graph are those within these cliques.
Return the graph as a list of edges (u, v) with 0 <= u < v < 10, or state "UNSATISFIABLE" if no graph... | false | null | {
"solve_time_ms": 8.9,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": -1,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 2.26,
"solve_pct_type": 41.67
} | null |
pysms_contains_cliques_clique_size4_num_cliques2_vertices15__v2 | pysms_contains_cliques | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": 15,
"max_clique": null,
"min_degree": null,
"clique_size": 4,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic... | Generate a graph with 15 vertices that consists of exactly 2 vertex-disjoint clique(s), each of size 4. Every vertex must belong to one of these cliques, and the only edges in the graph are those within these cliques.
Return the graph as a list of edges (u, v) with 0 <= u < v < 15, or state "UNSATISFIABLE" if no graph... | false | null | {
"solve_time_ms": 9.5,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": -1,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 3.2,
"solve_pct_type": 54.17
} | null |
pysms_contains_cliques_clique_size5_num_cliques1_vertices12__v1 | pysms_contains_cliques | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": 12,
"max_clique": null,
"min_degree": null,
"clique_size": 5,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic... | Generate a graph with 12 vertices that consists of exactly 1 vertex-disjoint clique(s), each of size 5. Every vertex must belong to one of these cliques, and the only edges in the graph are those within these cliques.
Return the graph as a list of edges (u, v) with 0 <= u < v < 12, or state "UNSATISFIABLE" if no graph... | false | null | {
"solve_time_ms": 8.4,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": -1,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 0.56,
"solve_pct_type": 4.17
} | null |
pysms_contains_cliques_clique_size5_num_cliques2_vertices13__v11 | pysms_contains_cliques | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": 13,
"max_clique": null,
"min_degree": null,
"clique_size": 5,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic... | Generate a graph with 13 vertices that consists of exactly 2 vertex-disjoint clique(s), each of size 5. Every vertex must belong to one of these cliques, and the only edges in the graph are those within these cliques.
Return the graph as a list of edges (u, v) with 0 <= u < v < 13, or state "UNSATISFIABLE" if no graph... | false | null | {
"solve_time_ms": 10,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": -1,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 4.7,
"solve_pct_type": 70.83
} | null |
pysms_contains_cliques_clique_size5_num_cliques2_vertices14__v9 | pysms_contains_cliques | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": 14,
"max_clique": null,
"min_degree": null,
"clique_size": 5,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic... | Generate a graph with 14 vertices that consists of exactly 2 vertex-disjoint clique(s), each of size 5. Every vertex must belong to one of these cliques, and the only edges in the graph are those within these cliques.
Return the graph as a list of edges (u, v) with 0 <= u < v < 14, or state "UNSATISFIABLE" if no graph... | false | null | {
"solve_time_ms": 9.6,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": -1,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 3.76,
"solve_pct_type": 62.5
} | null |
pysms_degree_bounds_max_degree3_min_degree1_vertices12__v10_h | pysms_degree_bounds | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": 12,
"max_clique": null,
"min_degree": 1,
"clique_size": null,
"max_degree": 3,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic_nu... | Generate a graph with 12 vertices where every vertex has degree between 1 and 3.
Return the graph as a list of edges (u, v) with 0 <= u < v < 12, or state "UNSATISFIABLE" if no graph exists.
Partial assignment (fixed values that must be respected):
- Known present edges: (2,9), (2,11), (2,10)
Return a complete soluti... | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
9
],
[
0,
10
],
[
0,
11
],
[
1,
9
],
[
1,
10
],
[
1,
11
],
[
2,
9
],
[
2,
10
],
[
... | {
"solve_time_ms": 22.5,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 18,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 12.97,
"solve_pct_type": 37.5
} | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
2,
9
],
[
2,
11
],
[
2,
10
]
],
"q": null
} |
pysms_degree_bounds_max_degree3_min_degree3_vertices11__v11 | pysms_degree_bounds | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": 11,
"max_clique": null,
"min_degree": 3,
"clique_size": null,
"max_degree": 3,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic_nu... | Generate a graph with 11 vertices where every vertex has degree between 3 and 3.
Return the graph as a list of edges (u, v) with 0 <= u < v < 11, or state "UNSATISFIABLE" if no graph exists. | false | null | {
"solve_time_ms": 130.3,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": -1,
"backend": "pysms",
"solve_tier": "medium",
"solve_pct_global": 46.8,
"solve_pct_type": 95.83
} | null |
pysms_degree_bounds_max_degree3_min_degree3_vertices12__v3_h | pysms_degree_bounds | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": 12,
"max_clique": null,
"min_degree": 3,
"clique_size": null,
"max_degree": 3,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic_nu... | Generate a graph with 12 vertices where every vertex has degree between 3 and 3.
Return the graph as a list of edges (u, v) with 0 <= u < v < 12, or state "UNSATISFIABLE" if no graph exists.
Partial assignment (fixed values that must be respected):
- Known present edges: (0,9), (1,10), (2,9)
Return a complete solutio... | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
9
],
[
0,
10
],
[
0,
11
],
[
1,
9
],
[
1,
10
],
[
1,
11
],
[
2,
9
],
[
2,
10
],
[
... | {
"solve_time_ms": 41.7,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 18,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 19.74,
"solve_pct_type": 54.17
} | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
9
],
[
1,
10
],
[
2,
9
]
],
"q": null
} |
pysms_degree_bounds_max_degree4_min_degree3_vertices10__v8_nh | pysms_degree_bounds | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": 10,
"max_clique": null,
"min_degree": 3,
"clique_size": null,
"max_degree": 4,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic_nu... | Generate a graph with 10 vertices where every vertex has degree between 3 and 4.
Return the graph as a list of edges (u, v) with 0 <= u < v < 10, or state "UNSATISFIABLE" if no graph exists. | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
7
],
[
0,
8
],
[
0,
9
],
[
1,
6
],
[
1,
7
],
[
1,
8
],
[
1,
9
],
[
2,
5
],
[
... | {
"solve_time_ms": 10.2,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 18,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 5.26,
"solve_pct_type": 4.17
} | null |
pysms_degree_bounds_max_degree5_min_degree1_vertices11__v1_h | pysms_degree_bounds | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": 11,
"max_clique": null,
"min_degree": 1,
"clique_size": null,
"max_degree": 5,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic_nu... | Generate a graph with 11 vertices where every vertex has degree between 1 and 5.
Return the graph as a list of edges (u, v) with 0 <= u < v < 11, or state "UNSATISFIABLE" if no graph exists.
Partial assignment (fixed values that must be respected):
- Known present edges: (2,8), (2,6), (2,10), (3,8), (0,10)
Return a c... | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
7
],
[
0,
8
],
[
0,
9
],
[
0,
10
],
[
1,
6
],
[
1,
7
],
[
1,
8
],
[
1,
9
],
[
... | {
"solve_time_ms": 17.6,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 26,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 9.59,
"solve_pct_type": 20.83
} | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
2,
8
],
[
2,
6
],
[
2,
10
],
[
3,
8
],
[
0,
10
]
],
"q": null
} |
pysms_degree_bounds_max_degree5_min_degree1_vertices15__v7_nh | pysms_degree_bounds | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": 15,
"max_clique": null,
"min_degree": 1,
"clique_size": null,
"max_degree": 5,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic_nu... | Generate a graph with 15 vertices where every vertex has degree between 1 and 5.
Return the graph as a list of edges (u, v) with 0 <= u < v < 15, or state "UNSATISFIABLE" if no graph exists. | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
10
],
[
0,
11
],
[
0,
12
],
[
0,
13
],
[
0,
14
],
[
1,
10
],
[
1,
11
],
[
1,
12
],
... | {
"solve_time_ms": 97.6,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 35,
"backend": "pysms",
"solve_tier": "medium",
"solve_pct_global": 38.53,
"solve_pct_type": 79.17
} | null |
pysms_degree_bounds_max_degree5_min_degree2_vertices15__v2_nh | pysms_degree_bounds | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": 15,
"max_clique": null,
"min_degree": 2,
"clique_size": null,
"max_degree": 5,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic_nu... | Generate a graph with 15 vertices where every vertex has degree between 2 and 5.
Return the graph as a list of edges (u, v) with 0 <= u < v < 15, or state "UNSATISFIABLE" if no graph exists. | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
10
],
[
0,
11
],
[
0,
12
],
[
0,
13
],
[
0,
14
],
[
1,
10
],
[
1,
11
],
[
1,
12
],
... | {
"solve_time_ms": 110,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 35,
"backend": "pysms",
"solve_tier": "medium",
"solve_pct_global": 45.3,
"solve_pct_type": 87.5
} | null |
pysms_degree_bounds_max_degree5_min_degree4_vertices13__v5_nh | pysms_degree_bounds | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": 13,
"max_clique": null,
"min_degree": 4,
"clique_size": null,
"max_degree": 5,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic_nu... | Generate a graph with 13 vertices where every vertex has degree between 4 and 5.
Return the graph as a list of edges (u, v) with 0 <= u < v < 13, or state "UNSATISFIABLE" if no graph exists. | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
9
],
[
0,
10
],
[
0,
11
],
[
0,
12
],
[
1,
8
],
[
1,
9
],
[
1,
10
],
[
1,
11
],
[
... | {
"solve_time_ms": 20,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 30,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 10.71,
"solve_pct_type": 29.17
} | null |
pysms_degree_bounds_max_degree5_min_degree4_vertices14__v9_h | pysms_degree_bounds | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": 14,
"max_clique": null,
"min_degree": 4,
"clique_size": null,
"max_degree": 5,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic_nu... | Generate a graph with 14 vertices where every vertex has degree between 4 and 5.
Return the graph as a list of edges (u, v) with 0 <= u < v < 14, or state "UNSATISFIABLE" if no graph exists.
Partial assignment (fixed values that must be respected):
- Known present edges: (1,11), (0,13), (7,9), (1,13), (4,11), (6,9)
R... | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
10
],
[
0,
11
],
[
0,
12
],
[
0,
13
],
[
1,
9
],
[
1,
10
],
[
1,
11
],
[
1,
12
],
... | {
"solve_time_ms": 16.2,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 33,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 8.08,
"solve_pct_type": 12.5
} | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
1,
11
],
[
0,
13
],
[
7,
9
],
[
1,
13
],
[
4,
11
],
[
6,
9
]
],
"q": null
} |
pysms_degree_bounds_max_degree6_min_degree3_vertices12__v6_nh | pysms_degree_bounds | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": 12,
"max_clique": null,
"min_degree": 3,
"clique_size": null,
"max_degree": 6,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic_nu... | Generate a graph with 12 vertices where every vertex has degree between 3 and 6.
Return the graph as a list of edges (u, v) with 0 <= u < v < 12, or state "UNSATISFIABLE" if no graph exists. | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
6
],
[
0,
7
],
[
0,
8
],
[
0,
9
],
[
0,
10
],
[
0,
11
],
[
1,
6
],
[
1,
7
],
[
... | {
"solve_time_ms": 90,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 36,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 31.95,
"solve_pct_type": 70.83
} | null |
pysms_degree_bounds_max_degree6_min_degree3_vertices14__v0_h | pysms_degree_bounds | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": 14,
"max_clique": null,
"min_degree": 3,
"clique_size": null,
"max_degree": 6,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic_nu... | Generate a graph with 14 vertices where every vertex has degree between 3 and 6.
Return the graph as a list of edges (u, v) with 0 <= u < v < 14, or state "UNSATISFIABLE" if no graph exists.
Partial assignment (fixed values that must be respected):
- Known present edges: (4,5), (0,10), (2,7), (6,8), (2,8), (1,6), (0,... | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
8
],
[
0,
9
],
[
0,
10
],
[
0,
11
],
[
0,
12
],
[
0,
13
],
[
1,
6
],
[
1,
7
],
[
... | {
"solve_time_ms": 56.8,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 42,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 23.87,
"solve_pct_type": 62.5
} | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
4,
5
],
[
0,
10
],
[
2,
7
],
[
6,
8
],
[
2,
8
],
[
1,
6
],
[
0,
9
],
[
5,
8
]
],
"q":... |
pysms_degree_bounds_max_degree6_min_degree4_vertices11__v4_h | pysms_degree_bounds | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": 11,
"max_clique": null,
"min_degree": 4,
"clique_size": null,
"max_degree": 6,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic_nu... | Generate a graph with 11 vertices where every vertex has degree between 4 and 6.
Return the graph as a list of edges (u, v) with 0 <= u < v < 11, or state "UNSATISFIABLE" if no graph exists.
Partial assignment (fixed values that must be respected):
- Known present edges: (5,6), (3,8), (0,9), (3,7), (3,9), (4,9)
Retur... | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
6
],
[
0,
7
],
[
0,
8
],
[
0,
9
],
[
0,
10
],
[
1,
6
],
[
1,
7
],
[
1,
8
],
[
... | {
"solve_time_ms": 32.9,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 32,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 17.48,
"solve_pct_type": 45.83
} | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
5,
6
],
[
3,
8
],
[
0,
9
],
[
3,
7
],
[
3,
9
],
[
4,
9
]
],
"q": null
} |
pysms_girth_degree_max_degree3_min_degree2_min_girth5_vertices10__v2_nh | pysms_girth_degree | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": 5,
"vertices": 10,
"max_clique": null,
"min_degree": 2,
"clique_size": null,
"max_degree": 3,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic_numbe... | Generate a graph with 10 vertices where the girth (shortest cycle) is at least 5 and every vertex has degree between 2 and 3.
Return the graph as a list of edges (u, v) with 0 <= u < v < 10, or state "UNSATISFIABLE" if no graph exists. | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
8
],
[
0,
9
],
[
1,
7
],
[
1,
9
],
[
2,
6
],
[
2,
9
],
[
3,
6
],
[
3,
7
],
[
... | {
"solve_time_ms": 11,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 12,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 5.83,
"solve_pct_type": 20.83
} | null |
pysms_girth_degree_max_degree3_min_degree3_min_girth5_vertices14__v4_nh | pysms_girth_degree | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": 5,
"vertices": 14,
"max_clique": null,
"min_degree": 3,
"clique_size": null,
"max_degree": 3,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic_numbe... | Generate a graph with 14 vertices where the girth (shortest cycle) is at least 5 and every vertex has degree between 3 and 3.
Return the graph as a list of edges (u, v) with 0 <= u < v < 14, or state "UNSATISFIABLE" if no graph exists. | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
11
],
[
0,
12
],
[
0,
13
],
[
1,
9
],
[
1,
10
],
[
1,
13
],
[
2,
8
],
[
2,
10
],
[... | {
"solve_time_ms": 23.1,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 21,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 13.35,
"solve_pct_type": 54.17
} | null |
pysms_girth_degree_max_degree4_min_degree4_min_girth4_vertices8__v3_h | pysms_girth_degree | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": 4,
"vertices": 8,
"max_clique": null,
"min_degree": 4,
"clique_size": null,
"max_degree": 4,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic_number... | Generate a graph with 8 vertices where the girth (shortest cycle) is at least 4 and every vertex has degree between 4 and 4.
Return the graph as a list of edges (u, v) with 0 <= u < v < 8, or state "UNSATISFIABLE" if no graph exists.
Partial assignment (fixed values that must be respected):
- Known present edges: (0,... | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
4
],
[
0,
5
],
[
0,
6
],
[
0,
7
],
[
1,
4
],
[
1,
5
],
[
1,
6
],
[
1,
7
],
[
... | {
"solve_time_ms": 9.9,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 16,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 4.32,
"solve_pct_type": 4.17
} | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
4
],
[
0,
7
],
[
2,
4
]
],
"q": null
} |
pysms_girth_degree_max_degree4_min_degree4_min_girth5_vertices8__v8 | pysms_girth_degree | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": 5,
"vertices": 8,
"max_clique": null,
"min_degree": 4,
"clique_size": null,
"max_degree": 4,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic_number... | Generate a graph with 8 vertices where the girth (shortest cycle) is at least 5 and every vertex has degree between 4 and 4.
Return the graph as a list of edges (u, v) with 0 <= u < v < 8, or state "UNSATISFIABLE" if no graph exists. | false | null | {
"solve_time_ms": 10.2,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": -1,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 5.26,
"solve_pct_type": 12.5
} | null |
pysms_girth_degree_max_degree5_min_degree2_min_girth4_vertices15__v6_h | pysms_girth_degree | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": 4,
"vertices": 15,
"max_clique": null,
"min_degree": 2,
"clique_size": null,
"max_degree": 5,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic_numbe... | Generate a graph with 15 vertices where the girth (shortest cycle) is at least 4 and every vertex has degree between 2 and 5.
Return the graph as a list of edges (u, v) with 0 <= u < v < 15, or state "UNSATISFIABLE" if no graph exists.
Partial assignment (fixed values that must be respected):
- Known present edges: (... | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
10
],
[
0,
11
],
[
0,
12
],
[
0,
13
],
[
0,
14
],
[
1,
10
],
[
1,
11
],
[
1,
12
],
... | {
"solve_time_ms": 96.9,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 31,
"backend": "pysms",
"solve_tier": "medium",
"solve_pct_global": 38.16,
"solve_pct_type": 79.17
} | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
2,
12
],
[
3,
10
],
[
6,
9
],
[
3,
13
],
[
3,
12
],
[
0,
13
]
],
"q": null
} |
pysms_girth_degree_max_degree5_min_degree2_min_girth6_vertices11__v0_nh | pysms_girth_degree | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": 6,
"vertices": 11,
"max_clique": null,
"min_degree": 2,
"clique_size": null,
"max_degree": 5,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic_numbe... | Generate a graph with 11 vertices where the girth (shortest cycle) is at least 6 and every vertex has degree between 2 and 5.
Return the graph as a list of edges (u, v) with 0 <= u < v < 11, or state "UNSATISFIABLE" if no graph exists. | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
9
],
[
0,
10
],
[
1,
8
],
[
1,
10
],
[
2,
7
],
[
2,
10
],
[
3,
6
],
[
3,
10
],
[
... | {
"solve_time_ms": 19.7,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 13,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 10.34,
"solve_pct_type": 37.5
} | null |
pysms_girth_degree_max_degree5_min_degree2_min_girth8_vertices9__v11_h | pysms_girth_degree | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": 8,
"vertices": 9,
"max_clique": null,
"min_degree": 2,
"clique_size": null,
"max_degree": 5,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic_number... | Generate a graph with 9 vertices where the girth (shortest cycle) is at least 8 and every vertex has degree between 2 and 5.
Return the graph as a list of edges (u, v) with 0 <= u < v < 9, or state "UNSATISFIABLE" if no graph exists.
Partial assignment (fixed values that must be respected):
- Known present edges: (2,... | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
7
],
[
0,
8
],
[
1,
6
],
[
1,
8
],
[
2,
5
],
[
2,
7
],
[
3,
4
],
[
3,
6
],
[
... | {
"solve_time_ms": 32,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 9,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 16.35,
"solve_pct_type": 62.5
} | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
2,
5
]
],
"q": null
} |
pysms_girth_degree_max_degree5_min_degree4_min_girth6_vertices16__v1 | pysms_girth_degree | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": 6,
"vertices": 16,
"max_clique": null,
"min_degree": 4,
"clique_size": null,
"max_degree": 5,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic_numbe... | Generate a graph with 16 vertices where the girth (shortest cycle) is at least 6 and every vertex has degree between 4 and 5.
Return the graph as a list of edges (u, v) with 0 <= u < v < 16, or state "UNSATISFIABLE" if no graph exists. | false | null | {
"solve_time_ms": 131.3,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": -1,
"backend": "pysms",
"solve_tier": "medium",
"solve_pct_global": 47.18,
"solve_pct_type": 87.5
} | null |
pysms_girth_degree_max_degree6_min_degree3_min_girth6_vertices12__v7 | pysms_girth_degree | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": 6,
"vertices": 12,
"max_clique": null,
"min_degree": 3,
"clique_size": null,
"max_degree": 6,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic_numbe... | Generate a graph with 12 vertices where the girth (shortest cycle) is at least 6 and every vertex has degree between 3 and 6.
Return the graph as a list of edges (u, v) with 0 <= u < v < 12, or state "UNSATISFIABLE" if no graph exists. | false | null | {
"solve_time_ms": 46.4,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": -1,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 21.8,
"solve_pct_type": 70.83
} | null |
pysms_girth_degree_max_degree6_min_degree3_min_girth6_vertices15__v10 | pysms_girth_degree | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": 6,
"vertices": 15,
"max_clique": null,
"min_degree": 3,
"clique_size": null,
"max_degree": 6,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic_numbe... | Generate a graph with 15 vertices where the girth (shortest cycle) is at least 6 and every vertex has degree between 3 and 6.
Return the graph as a list of edges (u, v) with 0 <= u < v < 15, or state "UNSATISFIABLE" if no graph exists. | false | null | {
"solve_time_ms": 188.2,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": -1,
"backend": "pysms",
"solve_tier": "medium",
"solve_pct_global": 49.06,
"solve_pct_type": 95.83
} | null |
pysms_girth_degree_max_degree6_min_degree3_min_girth7_vertices9__v5 | pysms_girth_degree | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": 7,
"vertices": 9,
"max_clique": null,
"min_degree": 3,
"clique_size": null,
"max_degree": 6,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic_number... | Generate a graph with 9 vertices where the girth (shortest cycle) is at least 7 and every vertex has degree between 3 and 6.
Return the graph as a list of edges (u, v) with 0 <= u < v < 9, or state "UNSATISFIABLE" if no graph exists. | false | null | {
"solve_time_ms": 21,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": -1,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 11.47,
"solve_pct_type": 45.83
} | null |
pysms_girth_degree_max_degree6_min_degree4_min_girth7_vertices8__v9 | pysms_girth_degree | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": 7,
"vertices": 8,
"max_clique": null,
"min_degree": 4,
"clique_size": null,
"max_degree": 6,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic_number... | Generate a graph with 8 vertices where the girth (shortest cycle) is at least 7 and every vertex has degree between 4 and 6.
Return the graph as a list of edges (u, v) with 0 <= u < v < 8, or state "UNSATISFIABLE" if no graph exists. | false | null | {
"solve_time_ms": 11.6,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": -1,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 6.58,
"solve_pct_type": 29.17
} | null |
pysms_graph_builder_Delta_upp2_delta_low1_max_chromatic_number2_min_chromatic_number2_num_edges_low9_num_edges_upp11_vertices12__v5_h | pysms_graph_builder | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": 2,
"min_edges": null,
"min_girth": null,
"vertices": 12,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic... | Generate a graph with 12 vertices that satisfies: minimum degree >= 1, maximum degree <= 2, edges between 9 and 11, chromatic number <= 2, chromatic number >= 2.
Return the graph as a list of edges (u, v) with 0 <= u < v < 12, or state "UNSATISFIABLE" if no graph exists.
Partial assignment (fixed values that must be ... | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
11
],
[
1,
9
],
[
1,
10
],
[
2,
8
],
[
2,
10
],
[
3,
7
],
[
3,
9
],
[
4,
6
],
[
... | {
"solve_time_ms": 20.7,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 11,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 11.09,
"solve_pct_type": 20.83
} | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
5,
7
],
[
4,
6
]
],
"q": null
} |
pysms_graph_builder_Delta_upp2_delta_low1_max_chromatic_number4_min_chromatic_number2_num_edges_low15_num_edges_upp12_vertices12__v3 | pysms_graph_builder | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": 4,
"min_edges": null,
"min_girth": null,
"vertices": 12,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic... | Generate a graph with 12 vertices that satisfies: minimum degree >= 1, maximum degree <= 2, edges between 15 and 12, chromatic number <= 4, chromatic number >= 2.
Return the graph as a list of edges (u, v) with 0 <= u < v < 12, or state "UNSATISFIABLE" if no graph exists. | false | null | {
"solve_time_ms": 96.6,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": -1,
"backend": "pysms",
"solve_tier": "medium",
"solve_pct_global": 37.22,
"solve_pct_type": 87.5
} | null |
pysms_graph_builder_Delta_upp2_delta_low2_max_chromatic_number4_min_chromatic_number2_num_edges_low9_num_edges_upp14_vertices13__v4_nh | pysms_graph_builder | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": 4,
"min_edges": null,
"min_girth": null,
"vertices": 13,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic... | Generate a graph with 13 vertices that satisfies: minimum degree >= 2, maximum degree <= 2, edges between 9 and 14, chromatic number <= 4, chromatic number >= 2.
Return the graph as a list of edges (u, v) with 0 <= u < v < 13, or state "UNSATISFIABLE" if no graph exists. | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
11
],
[
0,
12
],
[
1,
10
],
[
1,
12
],
[
2,
8
],
[
2,
9
],
[
3,
7
],
[
3,
9
],
[
... | {
"solve_time_ms": 46.9,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 13,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 22.37,
"solve_pct_type": 79.17
} | null |
pysms_graph_builder_Delta_upp3_delta_low2_max_chromatic_number4_min_chromatic_number2_num_edges_low12_num_edges_upp17_vertices9__v6_h | pysms_graph_builder | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": 4,
"min_edges": null,
"min_girth": null,
"vertices": 9,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic_... | Generate a graph with 9 vertices that satisfies: minimum degree >= 2, maximum degree <= 3, edges between 12 and 17, chromatic number <= 4, chromatic number >= 2.
Return the graph as a list of edges (u, v) with 0 <= u < v < 9, or state "UNSATISFIABLE" if no graph exists.
Partial assignment (fixed values that must be r... | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
7
],
[
0,
8
],
[
1,
6
],
[
1,
7
],
[
1,
8
],
[
2,
3
],
[
2,
4
],
[
2,
5
],
[
... | {
"solve_time_ms": 24.9,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 13,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 14.1,
"solve_pct_type": 37.5
} | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
8
],
[
6,
7
]
],
"q": null
} |
pysms_graph_builder_Delta_upp3_delta_low2_max_chromatic_number4_min_chromatic_number2_num_edges_low18_num_edges_upp10_vertices9__v7 | pysms_graph_builder | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": 4,
"min_edges": null,
"min_girth": null,
"vertices": 9,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic_... | Generate a graph with 9 vertices that satisfies: minimum degree >= 2, maximum degree <= 3, edges between 18 and 10, chromatic number <= 4, chromatic number >= 2.
Return the graph as a list of edges (u, v) with 0 <= u < v < 9, or state "UNSATISFIABLE" if no graph exists. | false | null | {
"solve_time_ms": 30,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": -1,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 15.98,
"solve_pct_type": 54.17
} | null |
pysms_graph_builder_Delta_upp3_delta_low2_max_chromatic_number4_min_chromatic_number2_num_edges_low9_num_edges_upp18_vertices9__v10_h | pysms_graph_builder | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": 4,
"min_edges": null,
"min_girth": null,
"vertices": 9,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic_... | Generate a graph with 9 vertices that satisfies: minimum degree >= 2, maximum degree <= 3, edges between 9 and 18, chromatic number <= 4, chromatic number >= 2.
Return the graph as a list of edges (u, v) with 0 <= u < v < 9, or state "UNSATISFIABLE" if no graph exists.
Partial assignment (fixed values that must be re... | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
7
],
[
0,
8
],
[
1,
5
],
[
1,
6
],
[
1,
8
],
[
2,
3
],
[
2,
4
],
[
2,
8
],
[
... | {
"solve_time_ms": 16.6,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 13,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 8.83,
"solve_pct_type": 4.17
} | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
5,
6
],
[
2,
3
]
],
"q": null
} |
pysms_graph_builder_Delta_upp3_delta_low3_max_chromatic_number2_min_chromatic_number2_num_edges_low16_num_edges_upp16_vertices8__v0 | pysms_graph_builder | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": 2,
"min_edges": null,
"min_girth": null,
"vertices": 8,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic_... | Generate a graph with 8 vertices that satisfies: minimum degree >= 3, maximum degree <= 3, edges between 16 and 16, chromatic number <= 2, chromatic number >= 2.
Return the graph as a list of edges (u, v) with 0 <= u < v < 8, or state "UNSATISFIABLE" if no graph exists. | false | null | {
"solve_time_ms": 18.3,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": -1,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 9.96,
"solve_pct_type": 12.5
} | null |
pysms_graph_builder_Delta_upp4_delta_low1_max_chromatic_number2_min_chromatic_number3_num_edges_low9_num_edges_upp17_vertices13__v1 | pysms_graph_builder | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": 2,
"min_edges": null,
"min_girth": null,
"vertices": 13,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic... | Generate a graph with 13 vertices that satisfies: minimum degree >= 1, maximum degree <= 4, edges between 9 and 17, chromatic number <= 2, chromatic number >= 3.
Return the graph as a list of edges (u, v) with 0 <= u < v < 13, or state "UNSATISFIABLE" if no graph exists. | false | null | {
"solve_time_ms": 979.8,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": -1,
"backend": "pysms",
"solve_tier": "hard",
"solve_pct_global": 67.48,
"solve_pct_type": 95.83
} | null |
pysms_graph_builder_Delta_upp4_delta_low2_max_chromatic_number3_min_chromatic_number3_num_edges_low14_num_edges_upp10_vertices8__v11 | pysms_graph_builder | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": 3,
"min_edges": null,
"min_girth": null,
"vertices": 8,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic_... | Generate a graph with 8 vertices that satisfies: minimum degree >= 2, maximum degree <= 4, edges between 14 and 10, chromatic number <= 3, chromatic number >= 3.
Return the graph as a list of edges (u, v) with 0 <= u < v < 8, or state "UNSATISFIABLE" if no graph exists. | false | null | {
"solve_time_ms": 27.6,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": -1,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 14.85,
"solve_pct_type": 45.83
} | null |
pysms_graph_builder_Delta_upp4_delta_low2_max_chromatic_number3_min_chromatic_number3_num_edges_low17_num_edges_upp11_vertices9__v9 | pysms_graph_builder | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": 3,
"min_edges": null,
"min_girth": null,
"vertices": 9,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic_... | Generate a graph with 9 vertices that satisfies: minimum degree >= 2, maximum degree <= 4, edges between 17 and 11, chromatic number <= 3, chromatic number >= 3.
Return the graph as a list of edges (u, v) with 0 <= u < v < 9, or state "UNSATISFIABLE" if no graph exists. | false | null | {
"solve_time_ms": 33.2,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": -1,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 18.05,
"solve_pct_type": 62.5
} | null |
pysms_graph_builder_Delta_upp4_delta_low3_max_chromatic_number3_min_chromatic_number2_num_edges_low13_num_edges_upp16_vertices8__v8_h | pysms_graph_builder | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": 3,
"min_edges": null,
"min_girth": null,
"vertices": 8,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic_... | Generate a graph with 8 vertices that satisfies: minimum degree >= 3, maximum degree <= 4, edges between 13 and 16, chromatic number <= 3, chromatic number >= 2.
Return the graph as a list of edges (u, v) with 0 <= u < v < 8, or state "UNSATISFIABLE" if no graph exists.
Partial assignment (fixed values that must be r... | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
5
],
[
0,
6
],
[
0,
7
],
[
1,
4
],
[
1,
6
],
[
1,
7
],
[
2,
4
],
[
2,
5
],
[
... | {
"solve_time_ms": 22.3,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 14,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 12.59,
"solve_pct_type": 29.17
} | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
1,
7
],
[
0,
7
]
],
"q": null
} |
pysms_graph_builder_Delta_upp5_delta_low3_max_chromatic_number4_min_chromatic_number3_num_edges_low7_num_edges_upp19_vertices11__v2_h | pysms_graph_builder | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": 4,
"min_edges": null,
"min_girth": null,
"vertices": 11,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic... | Generate a graph with 11 vertices that satisfies: minimum degree >= 3, maximum degree <= 5, edges between 7 and 19, chromatic number <= 4, chromatic number >= 3.
Return the graph as a list of edges (u, v) with 0 <= u < v < 11, or state "UNSATISFIABLE" if no graph exists.
Partial assignment (fixed values that must be ... | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
8
],
[
0,
9
],
[
0,
10
],
[
1,
8
],
[
1,
9
],
[
1,
10
],
[
2,
7
],
[
2,
8
],
[
... | {
"solve_time_ms": 43.1,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 19,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 20.11,
"solve_pct_type": 70.83
} | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
3,
7
],
[
2,
9
],
[
0,
9
]
],
"q": null
} |
pysms_independent_connectivity_max_independent_set2_min_connectivity1_vertices8__v2_nh | pysms_independent_connectivity | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": 8,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": 2,
"maximal_triangle_free": null,
"min_chromatic_... | Generate a graph with 8 vertices where the maximum independent set size is at most 2 and the vertex-connectivity is at least 1.
Return the graph as a list of edges (u, v) with 0 <= u < v < 8, or state "UNSATISFIABLE" if no graph exists. | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
1
],
[
0,
2
],
[
0,
3
],
[
0,
4
],
[
0,
5
],
[
0,
6
],
[
0,
7
],
[
1,
2
],
[
... | {
"solve_time_ms": 46.4,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 28,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 21.8,
"solve_pct_type": 4.17
} | null |
pysms_independent_connectivity_max_independent_set2_min_connectivity2_vertices9__v6_h | pysms_independent_connectivity | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": 9,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": 2,
"maximal_triangle_free": null,
"min_chromatic_... | Generate a graph with 9 vertices where the maximum independent set size is at most 2 and the vertex-connectivity is at least 2.
Return the graph as a list of edges (u, v) with 0 <= u < v < 9, or state "UNSATISFIABLE" if no graph exists.
Partial assignment (fixed values that must be respected):
- Known present edges: ... | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
1
],
[
0,
2
],
[
0,
3
],
[
0,
4
],
[
0,
5
],
[
0,
6
],
[
0,
7
],
[
0,
8
],
[
... | {
"solve_time_ms": 88.5,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 36,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 30.64,
"solve_pct_type": 20.83
} | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
3,
6
],
[
1,
4
],
[
0,
2
],
[
3,
8
],
[
1,
3
],
[
7,
8
],
[
5,
6
]
],
"q": null
} |
pysms_independent_connectivity_max_independent_set3_min_connectivity2_vertices10__v1_nh | pysms_independent_connectivity | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": 10,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": 3,
"maximal_triangle_free": null,
"min_chromatic... | Generate a graph with 10 vertices where the maximum independent set size is at most 3 and the vertex-connectivity is at least 2.
Return the graph as a list of edges (u, v) with 0 <= u < v < 10, or state "UNSATISFIABLE" if no graph exists. | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
1
],
[
0,
2
],
[
0,
3
],
[
0,
4
],
[
0,
5
],
[
0,
6
],
[
0,
7
],
[
0,
8
],
[
... | {
"solve_time_ms": 94.4,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 45,
"backend": "pysms",
"solve_tier": "medium",
"solve_pct_global": 34.96,
"solve_pct_type": 33.33
} | null |
pysms_independent_connectivity_max_independent_set3_min_connectivity4_vertices12__v8_nh | pysms_independent_connectivity | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": 12,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": 3,
"maximal_triangle_free": null,
"min_chromatic... | Generate a graph with 12 vertices where the maximum independent set size is at most 3 and the vertex-connectivity is at least 4.
Return the graph as a list of edges (u, v) with 0 <= u < v < 12, or state "UNSATISFIABLE" if no graph exists. | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
1
],
[
0,
2
],
[
0,
3
],
[
0,
4
],
[
0,
5
],
[
0,
6
],
[
0,
7
],
[
0,
8
],
[
... | {
"solve_time_ms": 601.5,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 66,
"backend": "pysms",
"solve_tier": "medium",
"solve_pct_global": 54.32,
"solve_pct_type": 87.5
} | null |
pysms_independent_connectivity_max_independent_set4_min_connectivity1_vertices9__v5_nh | pysms_independent_connectivity | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": 9,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": 4,
"maximal_triangle_free": null,
"min_chromatic_... | Generate a graph with 9 vertices where the maximum independent set size is at most 4 and the vertex-connectivity is at least 1.
Return the graph as a list of edges (u, v) with 0 <= u < v < 9, or state "UNSATISFIABLE" if no graph exists. | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
1
],
[
0,
2
],
[
0,
3
],
[
0,
4
],
[
0,
5
],
[
0,
6
],
[
0,
7
],
[
0,
8
],
[
... | {
"solve_time_ms": 80.9,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 36,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 26.13,
"solve_pct_type": 12.5
} | null |
pysms_independent_connectivity_max_independent_set4_min_connectivity3_vertices11__v3_h | pysms_independent_connectivity | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": 11,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": 4,
"maximal_triangle_free": null,
"min_chromatic... | Generate a graph with 11 vertices where the maximum independent set size is at most 4 and the vertex-connectivity is at least 3.
Return the graph as a list of edges (u, v) with 0 <= u < v < 11, or state "UNSATISFIABLE" if no graph exists.
Partial assignment (fixed values that must be respected):
- Known present edges... | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
1
],
[
0,
2
],
[
0,
3
],
[
0,
4
],
[
0,
5
],
[
0,
6
],
[
0,
7
],
[
0,
8
],
[
... | {
"solve_time_ms": 182.3,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 55,
"backend": "pysms",
"solve_tier": "medium",
"solve_pct_global": 48.31,
"solve_pct_type": 62.5
} | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
6
],
[
1,
10
],
[
3,
6
],
[
3,
8
],
[
2,
7
],
[
0,
4
],
[
1,
6
],
[
0,
8
],
[
... |
pysms_independent_connectivity_max_independent_set4_min_connectivity4_vertices11__v7_h | pysms_independent_connectivity | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": 11,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": 4,
"maximal_triangle_free": null,
"min_chromatic... | Generate a graph with 11 vertices where the maximum independent set size is at most 4 and the vertex-connectivity is at least 4.
Return the graph as a list of edges (u, v) with 0 <= u < v < 11, or state "UNSATISFIABLE" if no graph exists.
Partial assignment (fixed values that must be respected):
- Known present edges... | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
1
],
[
0,
2
],
[
0,
3
],
[
0,
4
],
[
0,
5
],
[
0,
6
],
[
0,
7
],
[
0,
8
],
[
... | {
"solve_time_ms": 368.5,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 55,
"backend": "pysms",
"solve_tier": "medium",
"solve_pct_global": 53.57,
"solve_pct_type": 79.17
} | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
5,
9
],
[
2,
7
],
[
1,
4
],
[
0,
8
],
[
1,
5
],
[
1,
9
],
[
6,
8
],
[
5,
6
],
[
... |
pysms_independent_connectivity_max_independent_set4_min_connectivity4_vertices15__v11_h | pysms_independent_connectivity | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": 15,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": 4,
"maximal_triangle_free": null,
"min_chromatic... | Generate a graph with 15 vertices where the maximum independent set size is at most 4 and the vertex-connectivity is at least 4.
Return the graph as a list of edges (u, v) with 0 <= u < v < 15, or state "UNSATISFIABLE" if no graph exists.
Partial assignment (fixed values that must be respected):
- Known present edges... | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
1
],
[
0,
2
],
[
0,
3
],
[
0,
4
],
[
0,
5
],
[
0,
6
],
[
0,
7
],
[
0,
8
],
[
... | {
"solve_time_ms": 2524.3,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 105,
"backend": "pysms",
"solve_tier": "hard",
"solve_pct_global": 93.05,
"solve_pct_type": 95.83
} | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
2,
5
],
[
8,
11
],
[
0,
2
],
[
5,
9
],
[
2,
10
],
[
2,
11
],
[
4,
13
],
[
7,
14
],
[
... |
pysms_independent_connectivity_max_independent_set4_min_connectivity4_vertices9__v0_nh | pysms_independent_connectivity | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": 9,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": 4,
"maximal_triangle_free": null,
"min_chromatic_... | Generate a graph with 9 vertices where the maximum independent set size is at most 4 and the vertex-connectivity is at least 4.
Return the graph as a list of edges (u, v) with 0 <= u < v < 9, or state "UNSATISFIABLE" if no graph exists. | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
1
],
[
0,
2
],
[
0,
3
],
[
0,
4
],
[
0,
5
],
[
0,
6
],
[
0,
7
],
[
0,
8
],
[
... | {
"solve_time_ms": 149.5,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 36,
"backend": "pysms",
"solve_tier": "medium",
"solve_pct_global": 47.93,
"solve_pct_type": 54.17
} | null |
pysms_independent_connectivity_max_independent_set5_min_connectivity1_vertices16__v4_h | pysms_independent_connectivity | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": 16,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": 5,
"maximal_triangle_free": null,
"min_chromatic... | Generate a graph with 16 vertices where the maximum independent set size is at most 5 and the vertex-connectivity is at least 1.
Return the graph as a list of edges (u, v) with 0 <= u < v < 16, or state "UNSATISFIABLE" if no graph exists.
Partial assignment (fixed values that must be respected):
- Known present edges... | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
1
],
[
0,
2
],
[
0,
3
],
[
0,
4
],
[
0,
5
],
[
0,
6
],
[
0,
7
],
[
0,
8
],
[
... | {
"solve_time_ms": 196,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 120,
"backend": "pysms",
"solve_tier": "medium",
"solve_pct_global": 49.44,
"solve_pct_type": 70.83
} | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
6,
14
],
[
13,
14
],
[
0,
12
],
[
2,
11
],
[
2,
10
],
[
8,
14
],
[
7,
14
],
[
6,
15
],
... |
pysms_independent_connectivity_max_independent_set5_min_connectivity2_vertices11__v10_nh | pysms_independent_connectivity | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": 11,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": 5,
"maximal_triangle_free": null,
"min_chromatic... | Generate a graph with 11 vertices where the maximum independent set size is at most 5 and the vertex-connectivity is at least 2.
Return the graph as a list of edges (u, v) with 0 <= u < v < 11, or state "UNSATISFIABLE" if no graph exists. | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
1
],
[
0,
2
],
[
0,
3
],
[
0,
4
],
[
0,
5
],
[
0,
6
],
[
0,
7
],
[
0,
8
],
[
... | {
"solve_time_ms": 106.3,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 55,
"backend": "pysms",
"solve_tier": "medium",
"solve_pct_global": 44.55,
"solve_pct_type": 45.83
} | null |
pysms_independent_connectivity_max_independent_set6_min_connectivity2_vertices10__v9_h | pysms_independent_connectivity | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": 10,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": 6,
"maximal_triangle_free": null,
"min_chromatic... | Generate a graph with 10 vertices where the maximum independent set size is at most 6 and the vertex-connectivity is at least 2.
Return the graph as a list of edges (u, v) with 0 <= u < v < 10, or state "UNSATISFIABLE" if no graph exists.
Partial assignment (fixed values that must be respected):
- Known present edges... | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
1
],
[
0,
2
],
[
0,
3
],
[
0,
4
],
[
0,
5
],
[
0,
6
],
[
0,
7
],
[
0,
8
],
[
... | {
"solve_time_ms": 94.4,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 45,
"backend": "pysms",
"solve_tier": "medium",
"solve_pct_global": 34.96,
"solve_pct_type": 33.33
} | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
3
],
[
3,
8
],
[
2,
9
],
[
0,
5
],
[
0,
4
],
[
1,
7
],
[
1,
4
],
[
1,
6
],
[
... |
pysms_min_connectivity_min_connectivity1_vertices14__v6_nh | pysms_min_connectivity | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": 14,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chroma... | Generate a graph with 14 vertices with vertex-connectivity at least 1.
Return the graph as a list of edges (u, v) with 0 <= u < v < 14, or state "UNSATISFIABLE" if no graph exists. | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
1
],
[
0,
2
],
[
0,
3
],
[
0,
4
],
[
0,
5
],
[
0,
6
],
[
0,
7
],
[
0,
8
],
[
... | {
"solve_time_ms": 98.5,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 91,
"backend": "pysms",
"solve_tier": "medium",
"solve_pct_global": 39.66,
"solve_pct_type": 20.83
} | null |
pysms_min_connectivity_min_connectivity1_vertices15__v3_nh | pysms_min_connectivity | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": 15,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chroma... | Generate a graph with 15 vertices with vertex-connectivity at least 1.
Return the graph as a list of edges (u, v) with 0 <= u < v < 15, or state "UNSATISFIABLE" if no graph exists. | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
1
],
[
0,
2
],
[
0,
3
],
[
0,
4
],
[
0,
5
],
[
0,
6
],
[
0,
7
],
[
0,
8
],
[
... | {
"solve_time_ms": 99.6,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 105,
"backend": "pysms",
"solve_tier": "medium",
"solve_pct_global": 41.54,
"solve_pct_type": 29.17
} | null |
pysms_min_connectivity_min_connectivity1_vertices8__v4_nh | pysms_min_connectivity | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": 8,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromat... | Generate a graph with 8 vertices with vertex-connectivity at least 1.
Return the graph as a list of edges (u, v) with 0 <= u < v < 8, or state "UNSATISFIABLE" if no graph exists. | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
1
],
[
0,
2
],
[
0,
3
],
[
0,
4
],
[
0,
5
],
[
0,
6
],
[
0,
7
],
[
1,
2
],
[
... | {
"solve_time_ms": 47.2,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 28,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 22.74,
"solve_pct_type": 4.17
} | null |
pysms_min_connectivity_min_connectivity1_vertices9__v10_h | pysms_min_connectivity | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": 9,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromat... | Generate a graph with 9 vertices with vertex-connectivity at least 1.
Return the graph as a list of edges (u, v) with 0 <= u < v < 9, or state "UNSATISFIABLE" if no graph exists.
Partial assignment (fixed values that must be respected):
- Known present edges: (2,6), (5,7), (2,5), (1,2), (4,6), (3,6), (1,5)
Return a c... | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
1
],
[
0,
2
],
[
0,
3
],
[
0,
4
],
[
0,
5
],
[
0,
6
],
[
0,
7
],
[
0,
8
],
[
... | {
"solve_time_ms": 80.4,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 36,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 25.38,
"solve_pct_type": 12.5
} | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
2,
6
],
[
5,
7
],
[
2,
5
],
[
1,
2
],
[
4,
6
],
[
3,
6
],
[
1,
5
]
],
"q": null
} |
pysms_min_connectivity_min_connectivity2_vertices16__v7_h | pysms_min_connectivity | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": 16,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chroma... | Generate a graph with 16 vertices with vertex-connectivity at least 2.
Return the graph as a list of edges (u, v) with 0 <= u < v < 16, or state "UNSATISFIABLE" if no graph exists.
Partial assignment (fixed values that must be respected):
- Known present edges: (5,13), (8,15), (1,4), (0,4), (8,10), (0,15), (3,10), (7... | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
1
],
[
0,
2
],
[
0,
3
],
[
0,
4
],
[
0,
5
],
[
0,
6
],
[
0,
7
],
[
0,
8
],
[
... | {
"solve_time_ms": 205.2,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 120,
"backend": "pysms",
"solve_tier": "medium",
"solve_pct_global": 50.19,
"solve_pct_type": 37.5
} | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
5,
13
],
[
8,
15
],
[
1,
4
],
[
0,
4
],
[
8,
10
],
[
0,
15
],
[
3,
10
],
[
7,
12
],
[... |
pysms_min_connectivity_min_connectivity2_vertices18__v1_nh | pysms_min_connectivity | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": 18,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chroma... | Generate a graph with 18 vertices with vertex-connectivity at least 2.
Return the graph as a list of edges (u, v) with 0 <= u < v < 18, or state "UNSATISFIABLE" if no graph exists. | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
1
],
[
0,
2
],
[
0,
3
],
[
0,
4
],
[
0,
5
],
[
0,
6
],
[
0,
7
],
[
0,
8
],
[
... | {
"solve_time_ms": 287.6,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 153,
"backend": "pysms",
"solve_tier": "medium",
"solve_pct_global": 52.44,
"solve_pct_type": 45.83
} | null |
pysms_min_connectivity_min_connectivity3_vertices14__v9_nh | pysms_min_connectivity | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": 14,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chroma... | Generate a graph with 14 vertices with vertex-connectivity at least 3.
Return the graph as a list of edges (u, v) with 0 <= u < v < 14, or state "UNSATISFIABLE" if no graph exists. | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
1
],
[
0,
2
],
[
0,
3
],
[
0,
4
],
[
0,
5
],
[
0,
6
],
[
0,
7
],
[
0,
8
],
[
... | {
"solve_time_ms": 481.5,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 91,
"backend": "pysms",
"solve_tier": "medium",
"solve_pct_global": 53.95,
"solve_pct_type": 62.5
} | null |
pysms_min_connectivity_min_connectivity3_vertices15__v0_nh | pysms_min_connectivity | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": 15,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chroma... | Generate a graph with 15 vertices with vertex-connectivity at least 3.
Return the graph as a list of edges (u, v) with 0 <= u < v < 15, or state "UNSATISFIABLE" if no graph exists. | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
1
],
[
0,
2
],
[
0,
3
],
[
0,
4
],
[
0,
5
],
[
0,
6
],
[
0,
7
],
[
0,
8
],
[
... | {
"solve_time_ms": 670.8,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 105,
"backend": "pysms",
"solve_tier": "medium",
"solve_pct_global": 55.08,
"solve_pct_type": 70.83
} | null |
pysms_min_connectivity_min_connectivity4_vertices11__v8_nh | pysms_min_connectivity | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": 11,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chroma... | Generate a graph with 11 vertices with vertex-connectivity at least 4.
Return the graph as a list of edges (u, v) with 0 <= u < v < 11, or state "UNSATISFIABLE" if no graph exists. | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
1
],
[
0,
2
],
[
0,
3
],
[
0,
4
],
[
0,
5
],
[
0,
6
],
[
0,
7
],
[
0,
8
],
[
... | {
"solve_time_ms": 365.7,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 55,
"backend": "pysms",
"solve_tier": "medium",
"solve_pct_global": 53.2,
"solve_pct_type": 54.17
} | null |
pysms_min_connectivity_min_connectivity4_vertices17__v2_nh | pysms_min_connectivity | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": 17,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chroma... | Generate a graph with 17 vertices with vertex-connectivity at least 4.
Return the graph as a list of edges (u, v) with 0 <= u < v < 17, or state "UNSATISFIABLE" if no graph exists. | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
1
],
[
0,
2
],
[
0,
3
],
[
0,
4
],
[
0,
5
],
[
0,
6
],
[
0,
7
],
[
0,
8
],
[
... | {
"solve_time_ms": 5677.6,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 136,
"backend": "pysms",
"solve_tier": "hard",
"solve_pct_global": 97.56,
"solve_pct_type": 79.17
} | null |
pysms_min_connectivity_min_connectivity4_vertices18__v11_h | pysms_min_connectivity | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": 18,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chroma... | Generate a graph with 18 vertices with vertex-connectivity at least 4.
Return the graph as a list of edges (u, v) with 0 <= u < v < 18, or state "UNSATISFIABLE" if no graph exists.
Partial assignment (fixed values that must be respected):
- Known present edges: (2,9), (0,10), (15,17), (12,15), (2,6), (3,17), (0,14), ... | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
1
],
[
0,
2
],
[
0,
3
],
[
0,
4
],
[
0,
5
],
[
0,
6
],
[
0,
7
],
[
0,
8
],
[
... | {
"solve_time_ms": 8143.1,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 153,
"backend": "pysms",
"solve_tier": "hard",
"solve_pct_global": 98.31,
"solve_pct_type": 87.5
} | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
2,
9
],
[
0,
10
],
[
15,
17
],
[
12,
15
],
[
2,
6
],
[
3,
17
],
[
0,
14
],
[
11,
13
],
... |
pysms_min_connectivity_min_connectivity5_vertices16__v5_h | pysms_min_connectivity | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": 16,
"max_clique": null,
"min_degree": null,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chroma... | Generate a graph with 16 vertices with vertex-connectivity at least 5.
Return the graph as a list of edges (u, v) with 0 <= u < v < 16, or state "UNSATISFIABLE" if no graph exists.
Partial assignment (fixed values that must be respected):
- Known present edges: (1,10), (4,10), (7,10), (1,6), (5,13), (3,6), (0,6), (0,... | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
1
],
[
0,
2
],
[
0,
3
],
[
0,
4
],
[
0,
5
],
[
0,
6
],
[
0,
7
],
[
0,
8
],
[
... | {
"solve_time_ms": 12188.6,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 120,
"backend": "pysms",
"solve_tier": "hard",
"solve_pct_global": 99.06,
"solve_pct_type": 95.83
} | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
1,
10
],
[
4,
10
],
[
7,
10
],
[
1,
6
],
[
5,
13
],
[
3,
6
],
[
0,
6
],
[
0,
15
],
[
... |
pysms_min_degree_min_degree1_vertices16__v4_nh | pysms_min_degree | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": 16,
"max_clique": null,
"min_degree": 1,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic... | Generate a graph with 16 vertices where the minimum degree is at least 1.
Return the graph as a list of edges (u, v) with 0 <= u < v < 16, or state "UNSATISFIABLE" if no graph exists. | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
1
],
[
0,
2
],
[
0,
3
],
[
0,
4
],
[
0,
5
],
[
0,
6
],
[
0,
7
],
[
0,
8
],
[
... | {
"solve_time_ms": 196.9,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 120,
"backend": "pysms",
"solve_tier": "medium",
"solve_pct_global": 49.81,
"solve_pct_type": 95.83
} | null |
pysms_min_degree_min_degree3_vertices11__v10_nh | pysms_min_degree | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": 11,
"max_clique": null,
"min_degree": 3,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic... | Generate a graph with 11 vertices where the minimum degree is at least 3.
Return the graph as a list of edges (u, v) with 0 <= u < v < 11, or state "UNSATISFIABLE" if no graph exists. | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
1
],
[
0,
2
],
[
0,
3
],
[
0,
4
],
[
0,
5
],
[
0,
6
],
[
0,
7
],
[
0,
8
],
[
... | {
"solve_time_ms": 85.4,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 55,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 28.38,
"solve_pct_type": 37.5
} | null |
pysms_min_degree_min_degree3_vertices12__v2_h | pysms_min_degree | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": 12,
"max_clique": null,
"min_degree": 3,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic... | Generate a graph with 12 vertices where the minimum degree is at least 3.
Return the graph as a list of edges (u, v) with 0 <= u < v < 12, or state "UNSATISFIABLE" if no graph exists.
Partial assignment (fixed values that must be respected):
- Known present edges: (7,9), (1,3), (0,8), (6,11), (1,6), (3,11), (4,9), (4... | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
1
],
[
0,
2
],
[
0,
3
],
[
0,
4
],
[
0,
5
],
[
0,
6
],
[
0,
7
],
[
0,
8
],
[
... | {
"solve_time_ms": 88.1,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 66,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 29.51,
"solve_pct_type": 45.83
} | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
7,
9
],
[
1,
3
],
[
0,
8
],
[
6,
11
],
[
1,
6
],
[
3,
11
],
[
4,
9
],
[
4,
11
],
[
... |
pysms_min_degree_min_degree3_vertices8__v11_h | pysms_min_degree | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": 8,
"max_clique": null,
"min_degree": 3,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic_... | Generate a graph with 8 vertices where the minimum degree is at least 3.
Return the graph as a list of edges (u, v) with 0 <= u < v < 8, or state "UNSATISFIABLE" if no graph exists.
Partial assignment (fixed values that must be respected):
- Known present edges: (2,6), (0,6), (4,7), (6,7), (3,7)
Return a complete sol... | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
1
],
[
0,
2
],
[
0,
3
],
[
0,
4
],
[
0,
5
],
[
0,
6
],
[
0,
7
],
[
1,
2
],
[
... | {
"solve_time_ms": 46.3,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 28,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 21.24,
"solve_pct_type": 4.17
} | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
2,
6
],
[
0,
6
],
[
4,
7
],
[
6,
7
],
[
3,
7
]
],
"q": null
} |
pysms_min_degree_min_degree4_vertices10__v9_h | pysms_min_degree | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": 10,
"max_clique": null,
"min_degree": 4,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic... | Generate a graph with 10 vertices where the minimum degree is at least 4.
Return the graph as a list of edges (u, v) with 0 <= u < v < 10, or state "UNSATISFIABLE" if no graph exists.
Partial assignment (fixed values that must be respected):
- Known present edges: (8,9), (2,8), (2,7), (2,9), (0,1), (0,8), (1,8), (3,8... | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
1
],
[
0,
2
],
[
0,
3
],
[
0,
4
],
[
0,
5
],
[
0,
6
],
[
0,
7
],
[
0,
8
],
[
... | {
"solve_time_ms": 88.3,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 45,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 30.26,
"solve_pct_type": 54.17
} | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
8,
9
],
[
2,
8
],
[
2,
7
],
[
2,
9
],
[
0,
1
],
[
0,
8
],
[
1,
8
],
[
3,
8
],
[
... |
pysms_min_degree_min_degree4_vertices9__v8_h | pysms_min_degree | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": 9,
"max_clique": null,
"min_degree": 4,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic_... | Generate a graph with 9 vertices where the minimum degree is at least 4.
Return the graph as a list of edges (u, v) with 0 <= u < v < 9, or state "UNSATISFIABLE" if no graph exists.
Partial assignment (fixed values that must be respected):
- Known present edges: (1,5), (0,1), (1,3), (3,6), (2,8), (4,5), (4,6)
Return ... | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
1
],
[
0,
2
],
[
0,
3
],
[
0,
4
],
[
0,
5
],
[
0,
6
],
[
0,
7
],
[
0,
8
],
[
... | {
"solve_time_ms": 80.5,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 36,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 25.75,
"solve_pct_type": 12.5
} | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
1,
5
],
[
0,
1
],
[
1,
3
],
[
3,
6
],
[
2,
8
],
[
4,
5
],
[
4,
6
]
],
"q": null
} |
pysms_min_degree_min_degree5_vertices13__v0_nh | pysms_min_degree | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": 13,
"max_clique": null,
"min_degree": 5,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic... | Generate a graph with 13 vertices where the minimum degree is at least 5.
Return the graph as a list of edges (u, v) with 0 <= u < v < 13, or state "UNSATISFIABLE" if no graph exists. | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
1
],
[
0,
2
],
[
0,
3
],
[
0,
4
],
[
0,
5
],
[
0,
6
],
[
0,
7
],
[
0,
8
],
[
... | {
"solve_time_ms": 89.6,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 78,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 31.39,
"solve_pct_type": 62.5
} | null |
pysms_min_degree_min_degree5_vertices18__v7_h | pysms_min_degree | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": 18,
"max_clique": null,
"min_degree": 5,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic... | Generate a graph with 18 vertices where the minimum degree is at least 5.
Return the graph as a list of edges (u, v) with 0 <= u < v < 18, or state "UNSATISFIABLE" if no graph exists.
Partial assignment (fixed values that must be respected):
- Known present edges: (3,15), (11,13), (13,17), (2,11), (11,17), (2,12), (7... | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
1
],
[
0,
2
],
[
0,
3
],
[
0,
4
],
[
0,
5
],
[
0,
6
],
[
0,
7
],
[
0,
8
],
[
... | {
"solve_time_ms": 108.8,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 153,
"backend": "pysms",
"solve_tier": "medium",
"solve_pct_global": 44.92,
"solve_pct_type": 87.5
} | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
3,
15
],
[
11,
13
],
[
13,
17
],
[
2,
11
],
[
11,
17
],
[
2,
12
],
[
7,
17
],
[
9,
17
],
... |
pysms_min_degree_min_degree5_vertices9__v1_h | pysms_min_degree | {
"n": null,
"k": null,
"p": null,
"max_chromatic_number": null,
"min_edges": null,
"min_girth": null,
"vertices": 9,
"max_clique": null,
"min_degree": 5,
"clique_size": null,
"max_degree": null,
"max_edges": null,
"max_independent_set": null,
"maximal_triangle_free": null,
"min_chromatic_... | Generate a graph with 9 vertices where the minimum degree is at least 5.
Return the graph as a list of edges (u, v) with 0 <= u < v < 9, or state "UNSATISFIABLE" if no graph exists.
Partial assignment (fixed values that must be respected):
- Known present edges: (5,7), (1,5), (3,6), (5,6), (4,5), (4,6), (0,7)
Return ... | true | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
0,
1
],
[
0,
2
],
[
0,
3
],
[
0,
4
],
[
0,
5
],
[
0,
6
],
[
0,
7
],
[
0,
8
],
[
... | {
"solve_time_ms": 81.3,
"search_space": -1,
"num_variables": -1,
"num_constraints": -1,
"num_edges": 36,
"backend": "pysms",
"solve_tier": "easy",
"solve_pct_global": 26.5,
"solve_pct_type": 20.83
} | {
"x": null,
"d": null,
"seq": null,
"c": null,
"edges": [
[
5,
7
],
[
1,
5
],
[
3,
6
],
[
5,
6
],
[
4,
5
],
[
4,
6
],
[
0,
7
]
],
"q": null
} |
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