{
  "id": "math/0312176",
  "version": "v2",
  "published": "2003-12-09T01:00:55.000Z",
  "updated": "2004-08-21T04:55:21.000Z",
  "title": "Intrinsic knotting and linking of almost complete partite graphs",
  "authors": [
    "Thomas W. Mattman",
    "Ryan Ottman",
    "Matt Rodrigues"
  ],
  "comment": "v2: 20 pages, 10 figures, substantial expansion of version 1",
  "categories": [
    "math.GT"
  ],
  "abstract": "We 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. For graphs in these families, we verify a conjecture presented in Adams' \"The Knot Book\": If a vertex is removed from an intrinsically knotted graph, one obtains an intrinsically linked graph.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2004-08-21T04:55:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C10",
      "57M15"
    ],
    "keywords": [
      "complete partite graphs",
      "intrinsic knotting",
      "edges short",
      "knot book",
      "classify graphs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math.....12176M"
    }
  }
}