{
  "id": "2205.09317",
  "version": "v1",
  "published": "2022-05-19T04:09:04.000Z",
  "updated": "2022-05-19T04:09:04.000Z",
  "title": "Odd coloring of two subclasses of planar graphs",
  "authors": [
    "Mengke Qi",
    "Xin Zhang"
  ],
  "comment": "11 pages, 2 figures",
  "categories": [
    "math.CO",
    "cs.DM"
  ],
  "abstract": "A proper coloring of a graph is odd if every non-isolated vertex has some color that appears an odd number of times on its neighborhood. Petru\\v{s}evski and \\v{S}krekovski conjectured in 2021 that every planar graph admits an odd $5$-coloring. We confirm this conjecture for outer-1-planar graphs and 2-boundary planar graphs, which are two subclasses of planar graphs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-05-19T04:09:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C15",
      "05C10"
    ],
    "keywords": [
      "odd coloring",
      "subclasses",
      "planar graph admits",
      "odd number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}