{
  "aliases": null,
  "backlinks": null,
  "body": "\n## Statement\n\n**Sumner's conjecture** (also called **Sumner's universal tournament conjecture**) is a conjecture in extremal graph theory on oriented [[trees|062D9KXJB1]] in tournaments. It states that every orientation of every $n$-vertex [[tree|062D9KXJB1]] is a subgraph of every $(2n-2)$-vertex tournament. David Sumner, a graph theorist at the University of South Carolina, conjectured in 1971 that tournaments are universal graphs for polytrees. The conjecture was proven for all large $n$ by Daniela Kühn, Richard Mycroft, and Deryk Osthus.\n",
  "commit": "68a8c3dc73fd55004b2796431c607c30960d1a85",
  "front": {
    "inventory": [
      "TZJPH47CRZ"
    ],
    "kind": "conjecture",
    "name": "Sumner's conjecture",
    "same_as": {
      "wikidata": "Q7637935",
      "wikipedia": "Sumner's conjecture"
    },
    "sources": [
      {
        "locator": "Sumner's conjecture",
        "mention": "wikipedia://en/28866227",
        "note": "adopted",
        "sections": [
          "Statement"
        ],
        "wikipedia": "en:28866227@r1315922689"
      }
    ],
    "tag": "12HP7ZS4D5"
  },
  "kind": "conjecture",
  "link": "https://math2.tamnd.com/node/12HP7ZS4D5/",
  "links": null,
  "markdown": "https://math2.tamnd.com/node/12HP7ZS4D5.md",
  "msc": null,
  "name": "Sumner's conjecture",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/12H/12HP7ZS4D5.md",
  "status": null,
  "tag": "12HP7ZS4D5",
  "uri": "m2://12HP7ZS4D5",
  "url": "https://math2.tamnd.com/wiki/sumners-conjecture/",
  "writing": {
    "tag": "12HP7ZS4D5",
    "kind": "conjecture",
    "level": "W0",
    "next": [
      {
        "what": "edge uses out",
        "have": 0,
        "want": 1
      }
    ]
  }
}