{
  "aliases": null,
  "backlinks": null,
  "body": "\n## Summary\n\nIn graph theory, a **bramble** for an undirected graph $G$ is a family of connected subgraphs of $G$ that all touch each other: for every pair of [[disjoint|0W4RPA8QH3]] subgraphs, there must exist an edge in $G$ that has one endpoint in each subgraph. The *order* of a bramble is the smallest size of a hitting set, a set of vertices of $G$ that has a nonempty intersection with each of the subgraphs. Brambles may be used to characterize the treewidth of $G$.\n",
  "commit": "68a8c3dc73fd55004b2796431c607c30960d1a85",
  "front": {
    "inventory": [
      "RR7667SGXJ"
    ],
    "kind": "concept",
    "name": "Bramble (graph theory)",
    "same_as": {
      "wikidata": "Q4956109",
      "wikipedia": "Bramble (graph theory)"
    },
    "sources": [
      {
        "locator": "Bramble (graph theory)",
        "mention": "wikipedia://en/36601188",
        "note": "adopted",
        "sections": [
          "Summary"
        ],
        "wikipedia": "en:36601188@r1335654220"
      }
    ],
    "tag": "ZZH60KP9WQ"
  },
  "kind": "concept",
  "link": "https://math2.tamnd.com/node/ZZH60KP9WQ/",
  "links": null,
  "markdown": "https://math2.tamnd.com/node/ZZH60KP9WQ.md",
  "msc": null,
  "name": "Bramble (graph theory)",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/ZZH/ZZH60KP9WQ.md",
  "status": null,
  "tag": "ZZH60KP9WQ",
  "uri": "m2://ZZH60KP9WQ",
  "url": "https://math2.tamnd.com/wiki/bramble-graph-theory/",
  "writing": {
    "tag": "ZZH60KP9WQ",
    "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
      }
    ]
  }
}