{
  "id": "1402.1813",
  "version": "v2",
  "published": "2014-02-08T03:21:34.000Z",
  "updated": "2014-08-05T21:01:18.000Z",
  "title": "Five-list-coloring graphs on surfaces I. Two lists of size two in planar graphs",
  "authors": [
    "Luke Postle",
    "Robin Thomas"
  ],
  "comment": "8 pages, minor revision based on referee report",
  "categories": [
    "math.CO",
    "cs.DM"
  ],
  "abstract": "Let G be a plane graph with outer cycle C, let u,v be vertices of C and let (L(x):x in V(G)) be a family of sets such that |L(u)|=|L(v)|=2, L(x) has at least three elements for every vertex x of C-{u,v} and L(x) has at least five elements for every vertex x of G-V(C). We prove a conjecture of Hutchinson that G has a (proper) coloring f such that f(x) belongs to L(x) for every vertex x of G. We will use this as a lemma in subsequent papers.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-08-05T21:01:18.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "planar graphs",
      "five-list-coloring graphs",
      "plane graph",
      "outer cycle",
      "subsequent papers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1402.1813P"
    }
  }
}