{
  "id": "2203.10239",
  "version": "v1",
  "published": "2022-03-19T04:35:01.000Z",
  "updated": "2022-03-19T04:35:01.000Z",
  "title": "Plane Triangulations Without Spanning 2-Trees",
  "authors": [
    "Allan Bickle"
  ],
  "comment": "9 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "A 2-tree is a graph that can be formed by starting with a triangle and iterating the operation of making a new vertex adjacent to two adjacent vertices of the existing graph. Leizhen Cai asked in 1995 whether every maximal planar graph contains a spanning 2-tree. We answer this question in the negative by constructing an infinite class of maximal planar graphs that have no spanning 2-tree.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-03-19T04:35:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C10"
    ],
    "keywords": [
      "plane triangulations",
      "maximal planar graph contains",
      "leizhen cai",
      "adjacent vertices",
      "vertex adjacent"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}