{
  "aliases": [
    "clique-cover-number",
    "clique-cover-problem",
    "clique-partition",
    "clique-partition-problem"
  ],
  "backlinks": null,
  "body": "\n## Summary\n\nIn graph theory, a **clique cover** or **partition into cliques** of a given undirected graph is a collection of [[cliques|0BYX1D7C2E]] that cover the whole graph. Generally, this means all vertices must be covered, and the term clique edge cover is used when all edges must be covered. A **minimum clique cover** is a clique cover that uses as few cliques as possible. The minimum $k$ for which a clique cover exists is called the **clique cover number** of the given graph.\n",
  "commit": "68a8c3dc73fd55004b2796431c607c30960d1a85",
  "front": {
    "aliases": [
      "clique-cover-number",
      "clique-cover-problem",
      "clique-partition",
      "clique-partition-problem"
    ],
    "inventory": [
      "MDDQM39AM8"
    ],
    "kind": "concept",
    "name": "Clique cover",
    "same_as": {
      "wikidata": "Q1096734",
      "wikipedia": "Clique cover"
    },
    "sources": [
      {
        "locator": "Clique cover",
        "mention": "wikipedia://en/17113364",
        "note": "adopted",
        "sections": [
          "Summary"
        ],
        "wikipedia": "en:17113364@r1321127633"
      }
    ],
    "tag": "74Q7PRTKVM"
  },
  "kind": "concept",
  "link": "https://math2.tamnd.com/node/74Q7PRTKVM/",
  "links": null,
  "markdown": "https://math2.tamnd.com/node/74Q7PRTKVM.md",
  "msc": null,
  "name": "Clique cover",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/74Q/74Q7PRTKVM.md",
  "status": null,
  "tag": "74Q7PRTKVM",
  "uri": "m2://74Q7PRTKVM",
  "url": "https://math2.tamnd.com/wiki/clique-cover/",
  "writing": {
    "tag": "74Q7PRTKVM",
    "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
      }
    ]
  }
}