{
  "id": "1002.4231",
  "version": "v2",
  "published": "2010-02-23T01:08:01.000Z",
  "updated": "2012-01-13T04:07:49.000Z",
  "title": "Triple crossing numbers of graphs",
  "authors": [
    "Hiroyuki Tanaka",
    "Masakazu Teragaito"
  ],
  "comment": "34 pages, 53 figures: We reorganized the article and revised some arguments",
  "categories": [
    "math.CO"
  ],
  "abstract": "We introduce the triple crossing number, a variation of crossing number, of a graph, which is the minimal number of crossing points in all drawings with only triple crossings of the graph. It is defined to be zero for a planar graph, and to be infinite unless a graph admits a drawing with only triple crossings. In this paper, we determine the triple crossing numbers for all complete multipartite graphs including all complete graphs.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-01-13T04:07:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C10"
    ],
    "keywords": [
      "triple crossing number",
      "complete multipartite graphs",
      "minimal number",
      "graph admits",
      "complete graphs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1002.4231T"
    }
  }
}