{
  "aliases": [
    "bipartite-kneser-graph",
    "generalized-kneser-graph",
    "kneser-conjecture",
    "kneser-graphs",
    "knesers-conjecture"
  ],
  "backlinks": null,
  "body": "\n## Summary\n\nIn graph theory, the **Kneser graph** $K(n, k)$ (alternatively $KG_{n,k}$) is the [[graph|00C0BR7D7H]] whose vertices correspond to the [[$k$-element subsets of a set of $n$ elements|098PHYBTV9]], and where two vertices are adjacent if and only if the two corresponding sets are [[disjoint|0W4RPA8QH3]]. Kneser graphs are named after Martin Kneser, who first investigated them in 1956.\n",
  "commit": "68a8c3dc73fd55004b2796431c607c30960d1a85",
  "front": {
    "aliases": [
      "bipartite-kneser-graph",
      "generalized-kneser-graph",
      "kneser-conjecture",
      "kneser-graphs",
      "knesers-conjecture"
    ],
    "inventory": [
      "2FCPX1W98H"
    ],
    "kind": "concept",
    "name": "Kneser graph",
    "same_as": {
      "wikidata": "Q733004",
      "wikipedia": "Kneser graph"
    },
    "sources": [
      {
        "locator": "Kneser graph",
        "mention": "wikipedia://en/2724154",
        "note": "adopted",
        "sections": [
          "Summary"
        ],
        "wikipedia": "en:2724154@r1362915729"
      }
    ],
    "tag": "DXHTCMW7E4"
  },
  "kind": "concept",
  "link": "https://math2.tamnd.com/node/DXHTCMW7E4/",
  "links": null,
  "markdown": "https://math2.tamnd.com/node/DXHTCMW7E4.md",
  "msc": null,
  "name": "Kneser graph",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/DXH/DXHTCMW7E4.md",
  "status": null,
  "tag": "DXHTCMW7E4",
  "uri": "m2://DXHTCMW7E4",
  "url": "https://math2.tamnd.com/wiki/kneser-graph/",
  "writing": {
    "tag": "DXHTCMW7E4",
    "kind": "concept",
    "level": "W1",
    "next": [
      {
        "what": "edge defines in",
        "note": "at least one definition",
        "have": 0,
        "want": 1
      },
      {
        "what": "edge instance_of in",
        "note": "at least two examples",
        "have": 0,
        "want": 2
      },
      {
        "what": "edge not_instance_of in",
        "note": "at least one non-example",
        "have": 0,
        "want": 1
      },
      {
        "what": "edge specializes both",
        "note": "the more general notions and the special cases",
        "have": 0,
        "want": 1
      }
    ]
  }
}