{
  "square_with_isolate_positive": {
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      "A",
      "B",
      "C",
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    ],
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        "B",
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      ],
      [
        "C",
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      ],
      [
        "D",
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    ],
    "result": {
      "bipartite": true,
      "colors": {
        "A": 0,
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        "D": 1,
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        "U": 0
      },
      "parent": {
        "A": null,
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      },
      "depth": {
        "A": 0,
        "B": 1,
        "D": 1,
        "C": 2,
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      },
      "partition": [
        [
          "A",
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        ],
        [
          "B",
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        ]
      ],
      "odd_closed_cycle": null,
      "trace": [
        {
          "action": "color",
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          "color": 1,
          "depth": 1
        },
        {
          "action": "color",
          "node": "D",
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        },
        {
          "action": "color",
          "node": "C",
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          "color": 0,
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        }
      ]
    }
  },
  "pentagon_with_isolate_negative": {
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    ],
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        "C",
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      ],
      [
        "D",
        "E"
      ],
      [
        "E",
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      ]
    ],
    "result": {
      "bipartite": false,
      "colors_partial": {
        "A": 0,
        "B": 1,
        "E": 1,
        "C": 0,
        "D": 0
      },
      "parent": {
        "A": null,
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      },
      "depth": {
        "A": 0,
        "B": 1,
        "E": 1,
        "C": 2,
        "D": 2
      },
      "conflict_edge": [
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      ],
      "odd_closed_cycle": [
        "C",
        "B",
        "A",
        "E",
        "D",
        "C"
      ],
      "trace": [
        {
          "action": "color",
          "node": "B",
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        },
        {
          "action": "color",
          "node": "E",
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        },
        {
          "action": "color",
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        },
        {
          "action": "color",
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          "color": 0,
          "depth": 2
        }
      ]
    }
  },
  "all1024_five_vertex_graph_coloring_oracles": {
    "cases": 1024,
    "bipartite": 376,
    "nonbipartite": 648,
    "oracle": "all2^5assignments independently tested per graph"
  },
  "empty_and_isolate_cases": [
    {
      "nodes": [],
      "edges": [],
      "result": {
        "bipartite": true,
        "colors": {},
        "parent": {},
        "depth": {},
        "partition": [
          [],
          []
        ],
        "odd_closed_cycle": null,
        "trace": []
      }
    },
    {
      "nodes": [
        "A",
        "B",
        "C"
      ],
      "edges": [],
      "result": {
        "bipartite": true,
        "colors": {
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        },
        "parent": {
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        },
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        },
        "partition": [
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          ],
          []
        ],
        "odd_closed_cycle": null,
        "trace": []
      }
    }
  ],
  "invalid_graphs_rejected": [
    "unknown",
    "parallel",
    "selfloop",
    "directed",
    "over_budget"
  ],
  "scope": "original BFS plus LCA reconstruction, not copied source DFS/Java run; closed odd-cycle certificate fully validated including nonancestor conflict endpoints; unweighted undirected simple graph only, not matching/stable marriage/SAT general solver or real object identity"
}