{
  "id": "1508.06892",
  "version": "v1",
  "published": "2015-08-27T15:05:13.000Z",
  "updated": "2015-08-27T15:05:13.000Z",
  "title": "On the Hamiltonian Number of a Planar Graph",
  "authors": [
    "Thomas M. Lewis"
  ],
  "comment": "11 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "The Hamiltonian number of a connected graph is the minimum of the lengths of the closed, spanning walks in the graph. In 1968, Grinberg published a necessary condition for the existence of a Hamiltonian cycle in a planar graph, formulated in terms of the lengths of its face cycles. We show how Grinberg's theorem can be adapted to provide a lower bound on the Hamiltonian number of a planar graph.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-08-27T15:05:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C10"
    ],
    "keywords": [
      "planar graph",
      "hamiltonian number",
      "lower bound",
      "grinbergs theorem",
      "face cycles"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}