{
  "id": "1906.05598",
  "version": "v1",
  "published": "2019-06-13T10:56:13.000Z",
  "updated": "2019-06-13T10:56:13.000Z",
  "title": "On Edge-Partitioning of Complete Geometric Graphs into Plane Trees",
  "authors": [
    "Hazim Michman Trao",
    "Gek L. Chia",
    "Niran Abbas Ali",
    "Adem Kilicman"
  ],
  "comment": "18 pages, 9 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "In response to a well-known open question ``Does every complete geometric graph on $2n\\/$ vertices have a partition of its edge set into $n\\/$ plane spanning trees?\" we provide an affirmative answer when the complete geometry graph is in the regular wheel configuration. Also we present sufficient conditions for the complete geometric graph on $2n\\/$ vertices to have a partition of its edge set into $n\\/$ plane spanning trees (which are double stars, caterpillars or $ w\\/$-caterpillars).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-13T10:56:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "complete geometric graph",
      "plane trees",
      "plane spanning trees",
      "edge set",
      "well-known open question"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}