{
  "id": "1707.02384",
  "version": "v1",
  "published": "2017-07-08T03:06:21.000Z",
  "updated": "2017-07-08T03:06:21.000Z",
  "title": "Disjoint cycles on Lichiardopol's conjecture in tournaments",
  "authors": [
    "Fuhong Ma",
    "Jin Yan"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "In this paper, we give an almost solution to the conjecture by N. Lichiardopol [Discrete Math. 310 (19) (2010) 2567-2570]. It is proved that for given integers $q \\geq 11$ and $k \\geq 1$, any tournament with minimum out-degree at least $(q-1)k-1$ contains at least $k$ disjoint cycles of length $q$. Our result is also an affirmative answer in terms of tournaments to the conjecture of C. Thomassen [Combinatorca. 3 (3-4) (1983) 393-396]. In addition, it is an extension of a result by J. Bang-Jensen, S. Bessy and S. Thomasse [J.Graph Theory 75 (3) (2014) 284-302].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-07-08T03:06:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "disjoint cycles",
      "lichiardopols conjecture",
      "tournament",
      "minimum out-degree",
      "graph theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}