{
  "id": "1101.4275",
  "version": "v2",
  "published": "2011-01-22T09:39:39.000Z",
  "updated": "2012-05-25T10:11:38.000Z",
  "title": "3-choosability of planar graphs with (<=4)-cycles far apart",
  "authors": [
    "Z. Dvorak"
  ],
  "comment": "59 pages, 7 figures; revised based on referee remarks",
  "categories": [
    "math.CO",
    "cs.DM"
  ],
  "abstract": "A graph is k-choosable if it can be colored whenever every vertex has a list of at least k available colors. We prove that if cycles of length at most four in a planar graph G are pairwise far apart, then G is 3-choosable. This is analogous to the problem of Havel regarding 3-colorability of planar graphs with triangles far apart.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-05-25T10:11:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C15",
      "G.2.2"
    ],
    "keywords": [
      "planar graph",
      "triangles far apart",
      "pairwise far apart"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 59,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}