{
  "id": "1006.0698",
  "version": "v4",
  "published": "2010-06-03T17:11:41.000Z",
  "updated": "2011-01-21T15:52:28.000Z",
  "title": "On intrinsically knotted or completely 3-linked graphs",
  "authors": [
    "Ryo Hanaki",
    "Ryo Nikkuni",
    "Kouki Taniyama",
    "Akiko Yamazaki"
  ],
  "comment": "17 pages, 9 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "We say that a graph is intrinsically knotted or completely 3-linked if every embedding of the graph into the 3-sphere contains a nontrivial knot or a 3-component link any of whose 2-component sublink is nonsplittable. We show that a graph obtained from the complete graph on seven vertices by a finite sequence of $\\triangle Y$-exchanges and $Y \\triangle$-exchanges is a minor-minimal intrinsically knotted or completely 3-linked graph.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2011-01-21T15:52:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M15",
      "57M25"
    ],
    "keywords": [
      "nontrivial knot",
      "complete graph",
      "seven vertices"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1006.0698H"
    }
  }
}