{
  "aliases": null,
  "backlinks": null,
  "body": "\n## Summary\n\nIn graph theory, the **Henson graph** $G_{i}$ is an undirected infinite graph, the unique countable homogeneous graph that does not contain an $i$-vertex [[clique|0BYX1D7C2E]] but that does contain all $K_{i}$-free finite graphs as induced subgraphs. For instance, $G_{3}$ is a triangle-free graph that contains all finite triangle-free graphs.\n",
  "commit": "68a8c3dc73fd55004b2796431c607c30960d1a85",
  "front": {
    "inventory": [
      "C1VZ02V7CS"
    ],
    "kind": "concept",
    "name": "Henson graph",
    "same_as": {
      "wikidata": "Q25304614",
      "wikipedia": "Henson graph"
    },
    "sources": [
      {
        "locator": "Henson graph",
        "mention": "wikipedia://en/49104628",
        "note": "adopted",
        "sections": [
          "Summary"
        ],
        "wikipedia": "en:49104628@r1280021819"
      }
    ],
    "tag": "TZT25G2YB3"
  },
  "kind": "concept",
  "link": "https://math2.tamnd.com/node/TZT25G2YB3/",
  "links": null,
  "markdown": "https://math2.tamnd.com/node/TZT25G2YB3.md",
  "msc": null,
  "name": "Henson graph",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/TZT/TZT25G2YB3.md",
  "status": null,
  "tag": "TZT25G2YB3",
  "uri": "m2://TZT25G2YB3",
  "url": "https://math2.tamnd.com/wiki/henson-graph/",
  "writing": {
    "tag": "TZT25G2YB3",
    "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
      }
    ]
  }
}
