{
  "name": "graceful_graph_k2_p4__v6_nh",
  "problem_type": "graceful_graph",
  "params": {
    "k": 2,
    "p": 4
  },
  "prompt": "Find a graceful labeling for the graph G_{2,4}: 4 disjoint K_2 cliques (numbered 0 through 3), 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 8 vertices and 10 edges in total.\n\nA graceful labeling assigns each vertex a unique label from 0 to 10 such that all edge labels |label(u) - label(v)| are distinct.\n\nReturn a list of 8 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": [
      0,
      2,
      10,
      3,
      1,
      7,
      9,
      4
    ],
    "d": [
      2,
      7,
      6,
      5,
      10,
      1,
      9,
      4,
      8,
      3
    ]
  },
  "difficulty": {
    "solve_time_ms": 1359.6,
    "search_space": 214358881,
    "num_variables": 18,
    "num_constraints": 14,
    "num_edges": -1,
    "backend": "pycsp",
    "solve_tier": "hard",
    "solve_pct_global": 83.65,
    "solve_pct_type": 56.25
  },
  "partial_assignment": null
}