File size: 1,392 Bytes
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"name": "graceful_graph_k3_p3__v5_nh",
"problem_type": "graceful_graph",
"params": {
"k": 3,
"p": 3
},
"prompt": "Find a graceful labeling for the graph G_{3,3}: 3 disjoint K_3 cliques (numbered 0 through 2), where each pair of consecutive cliques (g, g+1) is connected by 3 edges that link vertex i of clique g to vertex i of clique g+1 for each i in 0..2. The graph has 9 vertices and 15 edges in total.\n\nA graceful labeling assigns each vertex a unique label from 0 to 15 such that all edge labels |label(u) - label(v)| are distinct.\n\nReturn a list of 9 integers giving the vertex labels, ordered by clique then vertex within clique (so the i-th block of 3 consecutive entries gives the labels for clique i), or state \"UNSATISFIABLE\" if no such labeling exists.",
"satisfiable": true,
"solution": {
"x": [
2,
12,
0,
1,
6,
15,
14,
3,
7
],
"d": [
10,
2,
12,
5,
14,
9,
11,
7,
4,
1,
6,
15,
13,
3,
8
]
},
"difficulty": {
"solve_time_ms": 1302.4,
"search_space": 68719476736,
"num_variables": 24,
"num_constraints": 19,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 81.77,
"solve_pct_type": 43.75
},
"partial_assignment": null
} |