{
  "id": "1303.5156",
  "version": "v2",
  "published": "2013-03-21T03:59:00.000Z",
  "updated": "2013-03-22T02:53:13.000Z",
  "title": "Choosability of the square of a planar graph with maximum degree four",
  "authors": [
    "Daniel W. Cranston",
    "Rok Erman",
    "Riste Škrekovski"
  ],
  "comment": "14 pages, 6 figures; fixed typo",
  "categories": [
    "math.CO"
  ],
  "abstract": "We study squares of planar graphs with the aim to determine their list chromatic number. We present new upper bounds for the square of a planar graph with maximum degree $\\Delta \\leq 4$. In particular $G^2$ is 5-, 6-, 7-, 8-, 12-, 14-choosable if the girth of $G$ is at least 16, 11, 9, 7, 5, 3 respectively. In fact we prove more general results, in terms of maximum average degree, that imply the results above.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-03-22T02:53:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "planar graph",
      "maximum degree",
      "choosability",
      "maximum average degree",
      "list chromatic number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1303.5156C"
    }
  }
}