File size: 1,384 Bytes
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"name": "graceful_graph_k2_p5__v1_nh",
"problem_type": "graceful_graph",
"params": {
"k": 2,
"p": 5
},
"prompt": "Find a graceful labeling for the graph G_{2,5}: 5 disjoint K_2 cliques (numbered 0 through 4), where each pair of consecutive cliques (g, g+1) is connected by 2 edges that link vertex i of clique g to vertex i of clique g+1 for each i in 0..1. The graph has 10 vertices and 13 edges in total.\n\nA graceful labeling assigns each vertex a unique label from 0 to 13 such that all edge labels |label(u) - label(v)| are distinct.\n\nReturn a list of 10 integers giving the vertex labels, ordered by clique then vertex within clique (so the i-th block of 2 consecutive entries gives the labels for clique i), or state \"UNSATISFIABLE\" if no such labeling exists.",
"satisfiable": true,
"solution": {
"x": [
11,
6,
4,
10,
1,
2,
12,
0,
3,
13
],
"d": [
5,
6,
1,
12,
10,
7,
4,
3,
8,
11,
2,
9,
13
]
},
"difficulty": {
"solve_time_ms": 1003.9,
"search_space": 289254654976,
"num_variables": 23,
"num_constraints": 17,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 70.49,
"solve_pct_type": 6.25
},
"partial_assignment": null
} |