{
  "id": "0912.4770",
  "version": "v2",
  "published": "2009-12-24T20:24:37.000Z",
  "updated": "2011-03-08T16:51:05.000Z",
  "title": "Every plane graph of maximum degree 8 has an edge-face 9-colouring",
  "authors": [
    "Ross J. Kang",
    "Jean-Sébastien Sereni",
    "Matěj Stehlík"
  ],
  "comment": "29 pages, 1 figure; v2 corrects a contraction error in v1; to appear in SIDMA",
  "journal": "SIAM Journal on Discrete Mathematics 25(2): 514-533, 2011",
  "doi": "10.1137/090781206",
  "categories": [
    "math.CO"
  ],
  "abstract": "An edge-face colouring of a plane graph with edge set $E$ and face set $F$ is a colouring of the elements of $E \\cup F$ such that adjacent or incident elements receive different colours. Borodin proved that every plane graph of maximum degree $\\Delta\\ge10$ can be edge-face coloured with $\\Delta+1$ colours. Borodin's bound was recently extended to the case where $\\Delta=9$. In this paper, we extend it to the case $\\Delta=8$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-03-08T16:51:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C15"
    ],
    "keywords": [
      "plane graph",
      "maximum degree",
      "edge set",
      "borodins bound",
      "face set"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0912.4770K"
    }
  }
}