{
  "id": "1709.04608",
  "version": "v1",
  "published": "2017-09-14T04:15:14.000Z",
  "updated": "2017-09-14T04:15:14.000Z",
  "title": "Sufficient conditions on cycles that make planar graphs 4-choosable",
  "authors": [
    "Pongpat Sittitrai",
    "Kittikorn Nakprasit"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Xu and Wu proved that if every $5$-cycle of a planar graph $G$ is not simultaneously adjacent to $3$-cycles and $4$-cycles, then $G$ is $4$-choosable. In this paper, we improve this result as follows. Let $\\{i, j, k, l\\} = \\{3,4,5,6\\}.$ For any chosen $i,$ if every $i$-cycle of a planar graph $G$ is not simultaneously adjacent to $j$-cycles, $k$-cycles, and $l$-cycles, then $G$ is $4$-choosable.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-09-14T04:15:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C15",
      "G.2.2"
    ],
    "keywords": [
      "planar graph",
      "sufficient conditions",
      "simultaneously adjacent"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}