{
  "id": "1802.04179",
  "version": "v1",
  "published": "2018-02-12T16:47:21.000Z",
  "updated": "2018-02-12T16:47:21.000Z",
  "title": "Planar graphs without cycles of length 4 or 5 are (11:3)-colorable",
  "authors": [
    "Zdeněk Dvořák",
    "Xiaolan Hu"
  ],
  "comment": "23 pages, 5 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 show that every planar graph without cycles of length 4 or 5 is (11:3)-colorable, a weakening of recently disproved Steinberg's conjecture. In particular, each such graph with n vertices has an independent set of size at least 3n/11.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-02-12T16:47:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C15",
      "05C10",
      "G.2.2"
    ],
    "keywords": [
      "planar graph",
      "b-element subsets",
      "disproved steinbergs conjecture",
      "independent set",
      "adjacent vertices"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}