{
  "id": "1706.01699",
  "version": "v1",
  "published": "2017-06-06T11:17:50.000Z",
  "updated": "2017-06-06T11:17:50.000Z",
  "title": "Vertex-disjoint directed cycles of prescribed length in tournaments with given minimum out-degree",
  "authors": [
    "Maoqun Wang",
    "Weihua Yang"
  ],
  "comment": "8 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "The Bermond-Thomassen conjecture states that, for any positive integer $r$, a digraph of minimum out-degree at least $2r-1$ contains at least $r$ vertex-disjoint directed cycles. In 2014, Bang-Jensen, Bessy and Thomass\\' e proved the conjecture for tournaments. In 2010, Lichiardopol conjectured that a tournament $T$ with minimum out-degree at least $(q-1)r-1$ contains at least $r$ vertex-disjoint $q$-cycles, where integer $q\\geq3$ and $r\\geq1$. In this paper, we address Lichiardopol's conjecture affirmatively. In particular, the case $q=3$ implies Bermond-Thomassen conjecture for tournaments.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-06-06T11:17:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "vertex-disjoint directed cycles",
      "minimum out-degree",
      "prescribed length",
      "tournament",
      "address lichiardopols conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}