{
  "id": "1701.05597",
  "version": "v1",
  "published": "2017-01-19T20:54:51.000Z",
  "updated": "2017-01-19T20:54:51.000Z",
  "title": "Induced subgraphs of graphs with large chromatic number. VI. Banana trees",
  "authors": [
    "Alex Scott",
    "Paul Seymour"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We investigate which graphs H have the property that in every graph with bounded clique number and sufficiently large chromatic number, some induced subgraph is isomorphic to a subdivision of H. In an earlier paper, one of us proved that every tree has this property; and in another earlier paper with M. Chudnovsky, we proved that every cycle has this property. Here we give a common generalization. Say a banana is the union of a set of paths all with the same ends but otherwise disjoint. We prove that if H is obtained from a tree by replacing each edge by a banana then H has the property mentioned. We also find some other multigraphs with the same property.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-01-19T20:54:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "induced subgraph",
      "banana trees",
      "earlier paper",
      "sufficiently large chromatic number",
      "bounded clique number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}