{
  "aliases": null,
  "backlinks": [
    {
      "field": "proves",
      "target": "WQPR4SSA29"
    }
  ],
  "body": "\n## Statement\n\nIn graph theory, the **Gallai–Hasse–Roy–Vitaver theorem** is a form of [[duality|QS4283K3FK]] between the [[colorings|0NCPXH194Y]] of the vertices of a given undirected graph and the orientations of its edges. It states that the minimum number of colors needed to properly color any graph $G$ equals one plus the length of a longest path in an orientation of $G$ chosen to minimize this path's length. The orientations for which the longest path has minimum length always include at least one acyclic orientation.\n",
  "commit": "68a8c3dc73fd55004b2796431c607c30960d1a85",
  "front": {
    "inventory": [
      "D5F9TS715K"
    ],
    "kind": "statement",
    "name": "Gallai–Hasse–Roy–Vitaver theorem",
    "role": "proposition",
    "same_as": {
      "wikidata": "Q5518852",
      "wikipedia": "Gallai–Hasse–Roy–Vitaver theorem"
    },
    "sources": [
      {
        "locator": "Gallai–Hasse–Roy–Vitaver theorem",
        "mention": "wikipedia://en/36620043",
        "note": "adopted",
        "sections": [
          "Statement"
        ],
        "wikipedia": "en:36620043@r1345571774"
      }
    ],
    "tag": "CSS694B7NR"
  },
  "kind": "statement",
  "link": "https://math2.tamnd.com/node/CSS694B7NR/",
  "links": null,
  "markdown": "https://math2.tamnd.com/node/CSS694B7NR.md",
  "msc": null,
  "name": "Gallai–Hasse–Roy–Vitaver theorem",
  "prov": null,
  "role": "proposition",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/CSS/CSS694B7NR.md",
  "status": null,
  "tag": "CSS694B7NR",
  "uri": "m2://CSS694B7NR",
  "url": "https://math2.tamnd.com/wiki/gallai-hasse-roy-vitaver-theorem/",
  "writing": {
    "tag": "CSS694B7NR",
    "kind": "statement",
    "level": "W0",
    "next": [
      {
        "what": "edge uses out",
        "note": "each definition that the statement needs",
        "have": 0,
        "want": 1
      }
    ]
  }
}