{
  "id": "2402.03878",
  "version": "v1",
  "published": "2024-02-06T10:39:32.000Z",
  "updated": "2024-02-06T10:39:32.000Z",
  "title": "The generalizations of Hamiltonian in oriented graphs",
  "authors": [
    "Jia Zhou",
    "Zhilan Wang",
    "Jin Yan"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "An oriented graph is an orientation of a simple graph. In 2009, Keevash, K\\\"{u}hn and Osthus proved that every sufficiently large oriented graph $D$ of order $n$ with $(3n-4)/8$ is Hamiltonian. Later, Kelly, K\\\"{u}hn and Osthus showed that it is also pancyclic. Inspired by this, we show that for any given constant $t$ and positive integer partition $n = n_1 + \\cdots + n_t$, if $D$ is an oriented graph on $n$ vertices with minimum semidegree at least $(3n-4)/8$, then it contains $t$ disjoint cycles of lengths $n_1,\\ldots , n_t$. Also, we determine the bounds on the semidegree of sufficiently large oriented graphs that are strongly Hamiltonian-connected, $k$-ordered Hamiltonian and spanning $k$-linked.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-02-06T10:39:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C20",
      "05C38",
      "05C70"
    ],
    "keywords": [
      "sufficiently large oriented graph",
      "generalizations",
      "disjoint cycles",
      "simple graph",
      "positive integer partition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}