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"name": "graceful_graph_k2_p3__v0_h",
"problem_type": "graceful_graph",
"params": {
"k": 2,
"p": 3
},
"prompt": "Find a graceful labeling for the graph G_{2,3}: 3 disjoint K_2 cliques (numbered 0 through 2), 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 6 vertices and 7 edges in total.\n\nA graceful labeling assigns each vertex a unique label from 0 to 7 such that all edge labels |label(u) - label(v)| are distinct.\n\nReturn a list of 6 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.\n\nPartial assignment (fixed values that must be respected):\n- x[2]=7\n- d[6]=3\nReturn a complete solution consistent with these fixed assignments.",
"satisfiable": true,
"solution": {
"x": [
0,
2,
7,
3,
1,
6
],
"d": [
2,
4,
5,
7,
1,
6,
3
]
},
"difficulty": {
"solve_time_ms": 1025.2,
"search_space": 262144,
"num_variables": 13,
"num_constraints": 11,
"num_edges": -1,
"backend": "pycsp",
"solve_tier": "hard",
"solve_pct_global": 72.37,
"solve_pct_type": 18.75
},
"partial_assignment": {
"x": {
"2": 7
},
"d": {
"6": 3
}
}
} |