{
  "id": "1306.5283",
  "version": "v1",
  "published": "2013-06-22T02:36:14.000Z",
  "updated": "2013-06-22T02:36:14.000Z",
  "title": "On choosability with separation of planar graphs with lists of different sizes",
  "authors": [
    "Hal Kierstead",
    "Bernard Lidický"
  ],
  "comment": "7 pages, 2 figures",
  "categories": [
    "math.CO",
    "cs.DM"
  ],
  "abstract": "A (k,d)-list assignment L of a graph G is a mapping that assigns to each vertex v a list L(v) of at least k colors and for any adjacent pair xy, the lists L(x) and L(y) share at most d colors. A graph G is (k,d)-choosable if there exists an L-coloring of G for every (k,d)-list assignment L. This concept is also known as choosability with separation. It is known that planar graphs are (4,1)-choosable but it is not known if planar graphs are (3,1)-choosable. We strengthen the result that planar graphs are (4,1)-choosable by allowing an independent set of vertices to have lists of size 3 instead of 4.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-06-22T02:36:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C10",
      "05C15",
      "G.2.2"
    ],
    "keywords": [
      "planar graphs",
      "choosability",
      "separation",
      "adjacent pair xy",
      "assignment"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1306.5283K"
    }
  }
}