{
  "id": "1204.6457",
  "version": "v1",
  "published": "2012-04-29T06:23:35.000Z",
  "updated": "2012-04-29T06:23:35.000Z",
  "title": "Hamiltonicity in connected regular graphs",
  "authors": [
    "Daniel W. Cranston",
    "Suil O"
  ],
  "comment": "5 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "In 1980, Jackson proved that every 2-connected $k$-regular graph with at most $3k$ vertices is Hamiltonian. This result has been extended in several papers. In this note, we determine the minimum number of vertices in a connected $k$-regular graph that is not Hamiltonian, and we also solve the analogous problem for Hamiltonian paths. Further, we characterize the smallest connected $k$-regular graphs without a Hamiltonian cycle.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-04-29T06:23:35.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "connected regular graphs",
      "hamiltonicity",
      "hamiltonian cycle",
      "minimum number",
      "hamiltonian paths"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1204.6457C"
    }
  }
}