{
  "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
}