{
  "id": "1702.01094",
  "version": "v1",
  "published": "2017-02-03T17:44:43.000Z",
  "updated": "2017-02-03T17:44:43.000Z",
  "title": "Induced subgraphs of graphs with large chromatic number. IX. Rainbow paths",
  "authors": [
    "Alex Scott",
    "Paul Seymour"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We prove that for all nonnegative integers k,s there exists c with the following property. Let G be a graph with clique number at most k and chromatic number more than c. Then for every vertex-colouring (not necessarily optimal) of G, some induced subgraph of G is an s-vertex path, and all its vertices have different colours. This extends a recent result of Gyarfas and Sarkozy, who proved the same (when k=2) for graphs G with girth at least five.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-02-03T17:44:43.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "large chromatic number",
      "induced subgraph",
      "rainbow paths",
      "clique number",
      "s-vertex path"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}