{
  "aliases": null,
  "backlinks": null,
  "body": "\n## Definition\n\nLet $G$ be a finite [[graph|0JD5C82QMB]].\nThe clique number $\\omega(G)$ is the largest number of vertices of a [[clique|0G52BPNPKG]] in $G$.\n\n## Remarks\n\nThe vertices of a clique need different colours. Thus $\\omega(G) \\le \\chi(G)$, where $\\chi(G)$ is the [[chromatic number|0C5M7AM6FH]].\nFor the [[complete graph|03WKB2H474]], $\\omega(K_n) = n$. For the [[cycle graph|0QQ0F12962]] $C_n$ with $n \\ge 4$, $\\omega(C_n) = 2$.\nThe inequality $\\omega(G) \\le \\chi(G)$ can be strict: for $C_5$, $\\omega = 2$ and $\\chi = 3$.\n\n## Explanations\n\n### L1 human\n\nThe clique number is the size of the largest group of vertices that are all joined to each other.\nIt gives a lower bound for the number of colours that a graph needs.\n",
  "commit": "6ac761d40018146541484a9e8b9eafd6ecc303dc",
  "front": {
    "defines": "04MQSQ1F5Q",
    "kind": "definition",
    "msc": [
      "05C69"
    ],
    "name": "Clique number",
    "sources": [
      {
        "locator": "Definitions",
        "url": "https://en.wikipedia.org/wiki/Clique_(graph_theory)"
      }
    ],
    "tag": "0WCKRBHFFD",
    "uses": [
      "0G52BPNPKG"
    ]
  },
  "kind": "definition",
  "link": "https://math2.tamnd.com/node/0WCKRBHFFD/",
  "links": [
    {
      "field": "defines",
      "target": "04MQSQ1F5Q"
    },
    {
      "field": "uses",
      "target": "0G52BPNPKG"
    }
  ],
  "markdown": "https://math2.tamnd.com/node/0WCKRBHFFD.md",
  "msc": [
    "05C69"
  ],
  "name": "Clique number",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/0WC/0WCKRBHFFD.md",
  "status": null,
  "tag": "0WCKRBHFFD",
  "uri": "m2://0WCKRBHFFD",
  "url": "https://math2.tamnd.com/wiki/clique-number-definition/",
  "writing": {
    "tag": "0WCKRBHFFD",
    "kind": "definition",
    "level": "W0",
    "next": [
      {
        "what": "an inventory row",
        "note": "the row of the inventory that the node accounts for",
        "have": 0,
        "want": 1
      }
    ]
  }
}