{
  "id": "1409.2250",
  "version": "v1",
  "published": "2014-09-08T09:24:16.000Z",
  "updated": "2014-09-08T09:24:16.000Z",
  "title": "Colouring of plane graphs with unique maximal colours on faces",
  "authors": [
    "Alex Wendland"
  ],
  "comment": "10 pages, 9 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "The Four Colour Theorem asserts that the vertices of every plane graph can be properly coloured with four colors. Fabrici and G\\\"{o}ring conjectured the following stronger statement to also hold: the vertices of every plane graph can be properly coloured with the numbers 1,...,4 in such a way that every face contains a unique vertex coloured with the maximal color appearing on that face. They proved that every plane graph has such a colouring with the numbers 1,...,6. We prove that every plane graph has such a colouring with the numbers 1,...,5 and we also prove the list variant of the statement for lists of sizes seven.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-09-08T09:24:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "plane graph",
      "unique maximal colours",
      "colour theorem asserts",
      "maximal color",
      "stronger statement"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1409.2250W"
    }
  }
}