{
  "id": "2203.03612",
  "version": "v1",
  "published": "2022-03-07T18:59:32.000Z",
  "updated": "2022-03-07T18:59:32.000Z",
  "title": "Induced subgraphs of induced subgraphs of large chromatic number",
  "authors": [
    "António Girão",
    "Freddie Illingworth",
    "Emil Powierski",
    "Michael Savery",
    "Alex Scott",
    "Youri Tamitegama",
    "Jane Tan"
  ],
  "comment": "21 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "We prove that, for every graph $F$ with at least one edge, there is a constant $c_F$ such that there are graphs of arbitrarily large chromatic number and the same clique number as $F$ in which every $F$-free induced subgraph has chromatic number at most $c_F$. This generalises recent theorems of Bria\\'{n}ski, Davies and Walczak, and Carbonero, Hompe, Moore and Spirkl. Moreover, we show an analogous statement where clique number is replaced by odd girth.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-03-07T18:59:32.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "clique number",
      "arbitrarily large chromatic number",
      "odd girth",
      "free induced subgraph",
      "generalises"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}