{
  "id": "math/0611626",
  "version": "v1",
  "published": "2006-11-21T02:06:33.000Z",
  "updated": "2006-11-21T02:06:33.000Z",
  "title": "Counting Links in Complete Graphs",
  "authors": [
    "Tom Fleming",
    "Blake Mellor"
  ],
  "comment": "21 pages, several figures",
  "journal": "Osaka J. Math., vol. 46, 2009, pp. 1-29",
  "categories": [
    "math.CO",
    "math.GT"
  ],
  "abstract": "We find the minimal number of links in an embedding of any complete $k$-partite graph on 7 vertices (including $K_7$, which has at least 21 links). We give either exact values or upper and lower bounds for the minimal number of links for all complete $k$-partite graphs on 8 vertices. We also look at larger complete bipartite graphs, and state a conjecture relating minimal linking embeddings with minimal book embeddings.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-11-21T02:06:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C10",
      "57M15"
    ],
    "keywords": [
      "complete graphs",
      "counting links",
      "larger complete bipartite graphs",
      "minimal number",
      "minimal book embeddings"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....11626F"
    }
  }
}