{
  "id": "1809.07445",
  "version": "v1",
  "published": "2018-09-20T01:49:54.000Z",
  "updated": "2018-09-20T01:49:54.000Z",
  "title": "DP-3-coloring of planar graphs without $4,9$-cycles and two cycles from $\\{5,6,7,8\\}$",
  "authors": [
    "Runrun Liu",
    "Sarah Loeb",
    "Martin Rolek",
    "Yuxue Yin",
    "Gexin Yu"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "A generalization of list-coloring, now known as DP-coloring, was recently introduced by Dvo\\v{r}\\'{a}k and Postle. Essentially, DP-coloring assigns an arbitrary matching between lists of colors at adjacent vertices, as opposed to only matching identical colors as is done for list-coloring. Several results on list-coloring of planar graphs have since been extended to the setting of DP-coloring. We note that list-coloring results do not always extend to DP-coloring results. Our main result in this paper is to prove that every planar graph without cycles of length $\\{4, a, b, 9\\}$ for $a, b \\in \\{6, 7, 8\\}$ is DP-$3$-colorable, extending three existing results on $3$-choosability of planar graphs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-09-20T01:49:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "planar graph",
      "adjacent vertices",
      "main result",
      "generalization",
      "identical colors"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}