{
  "id": "2203.13460",
  "version": "v1",
  "published": "2022-03-25T05:53:13.000Z",
  "updated": "2022-03-25T05:53:13.000Z",
  "title": "Hamilton Cycles In Primitive Graphs of Order $2rs$",
  "authors": [
    "Shaofei Du",
    "Yao Tian",
    "Hao Yu"
  ],
  "comment": "22 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "After long term efforts, it was recently proved in \\cite{DKM2} that except for the Peterson graph, every connected vertex-transitive graph of order $rs$ has a Hamilton cycle, where $r$ and $s$ are primes. A natural topic is to solve the hamiltonian problem for connected vertex-transitive graphs of $2rs$. This topic is quite trivial, as the problem is still unsolved even for that of $r=3$. In this paper, it is shown that except for the Coxeter graph, every connected vertex-transitive graph of order $2rs$ contains a Hamilton cycle, provided the automorphism group acts primitively on vertices.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-03-25T05:53:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C25",
      "05C45"
    ],
    "keywords": [
      "hamilton cycle",
      "primitive graphs",
      "connected vertex-transitive graph",
      "long term efforts",
      "automorphism group acts"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}