{
  "id": "1306.5443",
  "version": "v1",
  "published": "2013-06-23T17:25:31.000Z",
  "updated": "2013-06-23T17:25:31.000Z",
  "title": "On Cayley digraphs that do not have hamiltonian paths",
  "authors": [
    "Dave Witte Morris"
  ],
  "comment": "10 pages, plus 14-page appendix of notes to aid the referee",
  "categories": [
    "math.CO"
  ],
  "abstract": "We construct an infinite family of connected, 2-generated Cayley digraphs Cay(G;a,b) that do not have hamiltonian paths, such that the orders of the generators a and b are arbitrarily large. We also prove that if G is any finite group with |[G,G]| < 4, then every connected Cayley digraph on G has a hamiltonian path (but the conclusion does not always hold when |[G,G]| = 4 or 5).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-06-23T17:25:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C20",
      "05C25",
      "05C45"
    ],
    "keywords": [
      "hamiltonian path",
      "cayley digraphs cay",
      "finite group",
      "connected cayley digraph",
      "generators"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1306.5443W"
    }
  }
}