{
  "id": "2306.16826",
  "version": "v1",
  "published": "2023-06-29T10:01:48.000Z",
  "updated": "2023-06-29T10:01:48.000Z",
  "title": "A new sufficient condition for a 2-strong digraph to be Hamiltonian",
  "authors": [
    "Samvel Kh. Darbinyan"
  ],
  "comment": "20 pages, 2 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "In this paper we prove the following new sufficient condition for a digraph to be Hamiltonian: {\\it Let $D$ be a 2-strong digraph of order $n\\geq 9$. If $n-1$ vertices of $D$ have degrees at least $n+k$ and the remaining vertex has degree at least $n-k-4$, where $k$ is a non-negative integer, then $D$ is Hamiltonian}. This is an extension of Ghouila-Houri's theorem for 2-strong digraphs and is a generalization of an early result of the author (DAN Arm. SSR (91(2):6-8, 1990). The obtained result is best possible in the sense that for $k=0$ there is a digraph of order $n=8$ (respectively, $n=9$) with the minimum degree $n-4=4$ (respectively, with the minimum $n-5=4$) whose $n-1$ vertices have degrees at least $n-1$, but it is not Hamiltonian. We also give a new sufficient condition for a 3-strong digraph to be Hamiltonian-connected.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-06-29T10:01:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "sufficient condition",
      "hamiltonian",
      "dan arm",
      "minimum degree",
      "ghouila-houris theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}