{
  "id": "2305.12041",
  "version": "v1",
  "published": "2023-05-19T23:54:37.000Z",
  "updated": "2023-05-19T23:54:37.000Z",
  "title": "Equitable coloring of planar graphs with maximum degree at least eight",
  "authors": [
    "Alexandr Kostochka",
    "Duo Lin",
    "Zimu Xiang"
  ],
  "comment": "20 pages, 2 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "The Chen-Lih-Wu Conjecture states that each connected graph with maximum degree $\\Delta\\geq 3$ that is not the complete graph $K_{\\Delta+1}$ or the complete bipartite graph $K_{\\Delta,\\Delta}$ admits an equitable coloring with $\\Delta$ colors. For planar graphs, the conjecture has been confirmed for $\\Delta\\geq 13$ by Yap and Zhang and for $9\\leq \\Delta\\leq 12$ by Nakprasit. In this paper, we present a proof that confirms the conjecture for graphs embeddable into a surface with non-negative Euler characteristic with maximum degree $\\Delta\\geq 9$ and for planar graphs with maximum degree $\\Delta\\geq 8$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-05-19T23:54:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C07",
      "05C10",
      "05C15"
    ],
    "keywords": [
      "maximum degree",
      "planar graphs",
      "equitable coloring",
      "chen-lih-wu conjecture states",
      "complete bipartite graph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}