{
  "id": "1804.04787",
  "version": "v1",
  "published": "2018-04-13T04:20:37.000Z",
  "updated": "2018-04-13T04:20:37.000Z",
  "title": "Unavoidable Subtournaments in Tournaments with Large Chromatic Number",
  "authors": [
    "Ilhee Kim",
    "Ringi Kim"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "For a set H of tournaments, we say H is heroic if every tournament, not containing any member of H as a subtournament, has bounded chromatic number. Berger et al. explicitly characterized all heroic sets containing one tournament. Motivated by this result, we study heroic sets containing two tournaments. We give a necessary condition for a set containing two tournaments to be heroic. We also construct infinitely many minimal heroic sets of size two.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-04-13T04:20:37.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "large chromatic number",
      "unavoidable subtournaments",
      "minimal heroic sets",
      "bounded chromatic number",
      "study heroic sets containing"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}