{
  "id": "math/0701422",
  "version": "v1",
  "published": "2007-01-15T19:09:46.000Z",
  "updated": "2007-01-15T19:09:46.000Z",
  "title": "Intrinsic knotting and linking of almost complete graphs",
  "authors": [
    "J. Campbell",
    "T. W. Mattman",
    "R. Ottman",
    "J. Pyzer",
    "M. Rodrigues",
    "S. Williams"
  ],
  "comment": "16 pages, 4 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "We introduce new sufficient conditions for intrinsic knotting and linking. A graph on n vertices with at least 4n-9 edges is intrinsically linked. A graph on n vertices with at least 5n-14 edges is intrinsically knotted. We also classify graphs that are 0, 1, or 2 edges short of being complete partite graphs with respect to intrinsic linking and intrinsic knotting. In addition, we classify intrinsic knotting of graphs on 8 vertices.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-01-15T19:09:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C10",
      "57M15",
      "05C35"
    ],
    "keywords": [
      "intrinsic knotting",
      "complete graphs",
      "complete partite graphs",
      "edges short",
      "sufficient conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math......1422C"
    }
  }
}