{
  "id": "2009.09881",
  "version": "v1",
  "published": "2020-09-21T14:00:31.000Z",
  "updated": "2020-09-21T14:00:31.000Z",
  "title": "The triangle-free graphs which are competition graphs of multipartite tournaments",
  "authors": [
    "Myungho Choi",
    "Minki Kwak",
    "Suh-Ryung Kim"
  ],
  "comment": "26 pages, 12 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "In this paper, we show that a connected triangle-free graph is the competition graph of a $k$-partite tournament if and only if $k \\in \\{3,4,5\\}$, and a disconnected triangle-free graph is the competition graph of a $k$-partite tournament if and only if $k \\in \\{2,3,4\\}$. Then we list all the triangle-free graphs in each case.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-09-21T14:00:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C20",
      "05C75"
    ],
    "keywords": [
      "competition graph",
      "multipartite tournaments",
      "disconnected triangle-free graph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}