{
  "id": "1608.00713",
  "version": "v1",
  "published": "2016-08-02T07:00:56.000Z",
  "updated": "2016-08-02T07:00:56.000Z",
  "title": "On the Minimum Number of Hamiltonian Cycles in Regular Graphs",
  "authors": [
    "Michael Haythorpe"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "A graph construction that produces a k-regular graph on n vertices for any choice of k >= 3 and n = m(k+1) for integer m >= 2 is described. The number of Hamiltonian cycles in such graphs can be explicitly determined as a function of n and k, and empirical evidence is provided that suggests that this function gives a tight upper bound on the minimum number of Hamiltonian cycles in k-regular graphs on n vertices for k >= 5 and n >= k + 3. An additional graph construction for 4-regular graphs is described for which the number of Hamiltonian cycles is superior to the above function in the case when k = 4 and n >= 11.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-08-02T07:00:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C35"
    ],
    "keywords": [
      "hamiltonian cycles",
      "minimum number",
      "regular graphs",
      "k-regular graph",
      "tight upper bound"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}