{
  "id": "2306.09655",
  "version": "v1",
  "published": "2023-06-16T07:18:28.000Z",
  "updated": "2023-06-16T07:18:28.000Z",
  "title": "A Note on Hamiltonian Cycles in Digraphs with Large Degrees",
  "authors": [
    "Samvel Kh. Darbinyan"
  ],
  "comment": "11 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "In this note we prove: {\\it Let $D$ be a 2-strong digraph of order $n$ such that its $n-1$ vertices have degrees at least $n+k$ and the remaining vertex $z$ has degree at least $n-k-4$, where $k$ is a positive integer. If $D$ contains a cycle of length at least $n-k-2$ passing through $z$, then $D$ is Hamiltonian}.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-06-16T07:18:28.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hamiltonian cycles",
      "large degrees",
      "positive integer"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}