{
  "id": "math/0110073",
  "version": "v1",
  "published": "2001-10-05T23:14:16.000Z",
  "updated": "2001-10-05T23:14:16.000Z",
  "title": "Hamiltonian Paths in Cartesian Powers of Directed Cycles",
  "authors": [
    "David Austin",
    "Heather Gavlas",
    "Dave Witte"
  ],
  "comment": "8 pages, no figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "The vertex set of the kth cartesian power of a directed cycle of length m can be naturally identified with the set of k-tuples of integers modulo m. For any two vertices v and w of this graph, it is easy to see that if there is a hamiltonian path from v to w, then the sum of the coordinates of v is congruent, modulo m, to one more than the sum of the coordinates of w. We prove the converse, unless k = 2 and m is odd.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2001-10-05T23:14:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C45",
      "05C25"
    ],
    "keywords": [
      "hamiltonian path",
      "directed cycle",
      "kth cartesian power",
      "integers modulo",
      "vertex set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math.....10073A"
    }
  }
}