{
  "id": "1404.6356",
  "version": "v2",
  "published": "2014-04-25T08:52:07.000Z",
  "updated": "2015-01-18T13:46:39.000Z",
  "title": "Three-coloring triangle-free graphs on surfaces IV. Bounding face sizes of 4-critical graphs",
  "authors": [
    "Zdenek Dvorak",
    "Daniel Kral",
    "Robin Thomas"
  ],
  "comment": "28 pages, 1 figure Several changes necessitated by further papers in the series included. Fixed an error: excluding only separating non-contractible 4-cycles is not enough. arXiv admin note: substantial text overlap with arXiv:1402.4710",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let G be a 4-critical graph with t triangles, embedded in a surface of genus g. Let c be the number of 4-cycles in G that do not bound a 2-cell face. We prove that the sum of lengths of (>=5)-faces of G is at most linear in g+t+c-1.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-04-25T08:52:07.000Z",
      "abstract": "Let G be a 4-critical graph with t triangles, embedded in a surface of genus g. Let c be the number of 4-cycles in G that separate the surface and do not bound a 2-cell face. We prove that the sum of lengths of (>=5)-faces of G is at most linear in g+t+c.",
      "comment": "28 pages, 1 figure",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-01-18T13:46:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C15",
      "05C10",
      "G.2.2"
    ],
    "keywords": [
      "bounding face sizes",
      "three-coloring triangle-free graphs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1404.6356D"
    }
  }
}