{
  "id": "1008.1085",
  "version": "v2",
  "published": "2010-08-05T21:04:09.000Z",
  "updated": "2013-06-21T05:45:31.000Z",
  "title": "Counting Links and Knots in Complete Graphs",
  "authors": [
    "Loren Abrams",
    "Blake Mellor",
    "Lowell Trott"
  ],
  "comment": "24 pages, 12 figures; v2 adds an appendix describing the program used to count the links and knots in examples",
  "categories": [
    "math.GT",
    "math.CO"
  ],
  "abstract": "We investigate the minimal number of links and knots in complete partite graphs. We provide exact values or bounds on the minimal number of links for all complete partite graphs with all but 4 vertices in one partition, or with 9 vertices in total. In particular, we find that the minimal number of links for $K_{4,4,1}$ is 74. We also provide exact values or bounds on the minimal number of knots for all complete partite graphs with 8 vertices.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-06-21T05:45:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M15",
      "57M27",
      "05C10"
    ],
    "keywords": [
      "complete partite graphs",
      "minimal number",
      "complete graphs",
      "counting links",
      "exact values"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1008.1085A"
    }
  }
}