{
  "id": "2311.13369",
  "version": "v1",
  "published": "2023-11-22T13:07:24.000Z",
  "updated": "2023-11-22T13:07:24.000Z",
  "title": "Note on Disjoint Cycles in Multipartite Tournaments",
  "authors": [
    "Gregory Gutin",
    "Wei Li",
    "Shujing Wang",
    "Anders Yeo",
    "Yacong Zhou"
  ],
  "comment": "9 pages, 0 figure",
  "categories": [
    "math.CO"
  ],
  "abstract": "In 1981, Bermond and Thomassen conjectured that for any positive integer $k$, every digraph with minimum out-degree at least $2k-1$ admits $k$ vertex-disjoint directed cycles. In this short paper, we verify the Bermond-Thomassen conjecture for triangle-free multipartite tournaments and 3-partite tournaments. Furthermore, we characterize 3-partite tournaments with minimum out-degree at least $2k-1$ ($k\\geq 2$) such that in each set of $k$ vertex-disjoint directed cycles, every cycle has the same length.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-11-22T13:07:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C20",
      "05C75"
    ],
    "keywords": [
      "disjoint cycles",
      "vertex-disjoint directed cycles",
      "minimum out-degree",
      "triangle-free multipartite tournaments",
      "bermond-thomassen conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}