{
  "id": "1608.03105",
  "version": "v1",
  "published": "2016-08-10T09:32:38.000Z",
  "updated": "2016-08-10T09:32:38.000Z",
  "title": "Hamiltonian cycles in some family of cubic $3$-connected plane graphs",
  "authors": [
    "Jan Florek"
  ],
  "comment": "29 pages, 28 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "Barnette conjectured that all cubic $3$-connected plane graphs with maximum face size at most $6$ are hamiltonian. We provide a method of construction of a hamiltonian cycle (in dual terms) in an arbitrary cubic, $3$-connected plane graph possessing such a face $g$ that every face incident with $g$ has at most $5$ edges and every other face has at most $6$ edges.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-08-10T09:32:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C45",
      "05C05"
    ],
    "keywords": [
      "hamiltonian cycle",
      "face incident",
      "dual terms",
      "arbitrary cubic",
      "maximum face size"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}