{
  "id": "1809.05439",
  "version": "v1",
  "published": "2018-09-14T14:26:15.000Z",
  "updated": "2018-09-14T14:26:15.000Z",
  "title": "Fractional coloring of planar graphs of girth five",
  "authors": [
    "Zdeněk Dvořák",
    "Xiaolan Hu"
  ],
  "comment": "19 pages, 3 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "A graph G is (a:b)-colorable if there exists an assignment of b-element subsets of {1,...,a} to vertices of G such that sets assigned to adjacent vertices are disjoint. We first show that for every triangle-free planar graph G and a vertex x of G, the graph G has a set coloring phi by subsets of {1,...,6} such that |phi(v)|>=2 for each vertex v of G and |phi(x)|=3. As a corollary, every triangle-free planar graph on n vertices is (6n:2n+1)-colorable. We further use this result to prove that for every Delta, there exists a constant M_Delta such that every planar graph G of girth at least five and maximum degree Delta is (6M_Delta:2M_Delta+1)-colorable. Consequently, planar graphs of girth at least five with bounded maximum degree Delta have fractional chromatic number at most 3-3/(2M_Delta+1).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-09-14T14:26:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C15",
      "05C10",
      "G.2.2"
    ],
    "keywords": [
      "triangle-free planar graph",
      "fractional coloring",
      "bounded maximum degree delta",
      "fractional chromatic number",
      "b-element subsets"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}