{
  "id": "1711.08612",
  "version": "v1",
  "published": "2017-11-23T08:32:11.000Z",
  "updated": "2017-11-23T08:32:11.000Z",
  "title": "Induced subgraphs of graphs with large chromatic number. XII. Distant stars",
  "authors": [
    "Maria Chudnovsky",
    "Alex Scott",
    "Paul Seymour"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "The Gyarfas-Sumner conjecture asserts that if H is a tree then every graph with bounded clique number and very large chromatic number contains H as an induced subgraph. This is still open, although it has been proved for a few simple families of trees, including trees of radius two, some special trees of radius three, and subdivided stars. These trees all have the property that their vertices of degree more than two are clustered quite closely together. In this paper, we prove the conjecture for two families of trees which do not have this restriction.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-11-23T08:32:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "induced subgraph",
      "distant stars",
      "large chromatic number contains",
      "gyarfas-sumner conjecture asserts",
      "bounded clique number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}