{
  "id": "2309.10876",
  "version": "v1",
  "published": "2023-09-19T18:57:14.000Z",
  "updated": "2023-09-19T18:57:14.000Z",
  "title": "On Vizing's problem for triangle-free graphs",
  "authors": [
    "Ross J. Kang",
    "Matthieu Rosenfeld"
  ],
  "comment": "10 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "We prove that $\\chi(G) \\le \\lceil (\\Delta+1)/2\\rceil+1$ for any triangle-free graph $G$ of maximum degree $\\Delta$ provided $\\Delta \\ge 524$. This gives tangible progress towards an old problem of Vizing, in a form cast by Reed. We use a method of Hurley and Pirot, which in turn relies on a new counting argument of the second author.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-09-19T18:57:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C15",
      "05C35"
    ],
    "keywords": [
      "triangle-free graph",
      "vizings problem",
      "maximum degree",
      "second author",
      "form cast"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}