{
  "id": "2107.03585",
  "version": "v1",
  "published": "2021-07-08T03:40:41.000Z",
  "updated": "2021-07-08T03:40:41.000Z",
  "title": "Improved bounds for colouring circle graphs",
  "authors": [
    "James Davies"
  ],
  "comment": "16 pages, 3 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "We prove the first $\\chi$-bounding function for circle graphs that is optimal up to a constant factor. To be more precise, we prove that every circle graph with clique number at most $\\omega$ has chromatic number at most $2\\omega \\log_2 (\\omega) +2\\omega \\log_2(\\log_2 (\\omega)) + 10\\omega$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-07-08T03:40:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C15",
      "05C62"
    ],
    "keywords": [
      "colouring circle graphs",
      "clique number",
      "chromatic number",
      "constant factor"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}