{
  "id": "2401.07776",
  "version": "v1",
  "published": "2024-01-15T15:37:34.000Z",
  "updated": "2024-01-15T15:37:34.000Z",
  "title": "Computing the clique number of tournaments",
  "authors": [
    "Guillaume Aubian"
  ],
  "categories": [
    "math.CO",
    "cs.DM"
  ],
  "abstract": "The clique number of a tournament is the maximum clique number of a graph formed by keeping backwards arcs in an ordering of its vertices. We study the time complexity of computing the clique number of a tournament and prove that, for any integer $k \\geq 3$, deciding whether a tournament has clique number at most $k$ is NP-complete. This answers an interrogation of Nguyen, Scott and Seymour. To do so, we make use of a construction which we then modify to provide a counterexample to a conjecture of Aboulker, Aubian, Charbit and Lopes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-01-15T15:37:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "tournament",
      "maximum clique number",
      "time complexity",
      "np-complete",
      "keeping backwards arcs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}