{
  "id": "2506.19888",
  "version": "v1",
  "published": "2025-06-24T07:04:28.000Z",
  "updated": "2025-06-24T07:04:28.000Z",
  "title": "Hamilton Cycles In Vertex-Transitive Graphs of Order 10p",
  "authors": [
    "Huye Chen",
    "Jingjian Li",
    "Hao Yu"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "After a long term efforts, the Hamiltonian problem of connected vertex-transitive graphs of order $pq$ (where $p$ and $q$ are primes) was finally finshed in 2021, see [10]. Fifteen years ago, mathematicians began to challenge this problem for graphs of order $2pq$. Among of them, it was proved in 2012 (see [21]) that every connected vertex-transitive graph of order $10p$ (where $p\\neq7$ is a prime) contains a Hamilton path, with the exception of a family of graphs which was recently confirmed in [11]. In this paper, a further conclusion will be achieved: every connected vertex-transitive graph of order $10p$ (where $p$ is a prime) contains a Hamilton cycle, except for the truncation of the Petersen graph.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-06-24T07:04:28.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hamilton cycle",
      "order 10p",
      "connected vertex-transitive graph",
      "long term efforts",
      "petersen graph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}