{
  "id": "2102.06993",
  "version": "v1",
  "published": "2021-02-13T19:52:06.000Z",
  "updated": "2021-02-13T19:52:06.000Z",
  "title": "The choice number versus the chromatic number for graphs embeddable on orientable surfaces",
  "authors": [
    "Niranjan Balachandran",
    "Brahadeesh Sankarnarayanan"
  ],
  "comment": "17 pages, 6 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "We show that for loopless $6$-regular triangulations on the torus the gap between the choice number and chromatic number is at most $2$. We also show that the largest gap for graphs embeddable in an orientable surface of genus $g$ is of the order $\\Theta(\\sqrt{g})$, and moreover for graphs with chromatic number of the order $o(\\sqrt{g}/\\log(g))$ the largest gap is of the order $o(\\sqrt{g})$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-13T19:52:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C15",
      "05C10",
      "05C35",
      "05C75"
    ],
    "keywords": [
      "chromatic number",
      "choice number",
      "orientable surface",
      "graphs embeddable"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}