{
  "id": "2208.14860",
  "version": "v1",
  "published": "2022-08-31T13:42:34.000Z",
  "updated": "2022-08-31T13:42:34.000Z",
  "title": "Chi-boundedness of graphs containing no cycles with $k$ chords",
  "authors": [
    "Joonkyung Lee",
    "Shoham Letzter",
    "Alexey Pokrvoskiy"
  ],
  "comment": "38 pages, 13 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "We prove that the family of graphs containing no cycle with exactly $k$-chords is $\\chi$-bounded, for $k$ large enough or of form $\\ell(\\ell-2)$ with $\\ell \\ge 3$ an integer. This verifies (up to a finite number of values $k$) a conjecture of Aboulker and Bousquet (2015).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-08-31T13:42:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "graphs containing",
      "chi-boundedness",
      "finite number",
      "conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}