{
  "id": "2312.09873",
  "version": "v1",
  "published": "2023-12-15T15:20:01.000Z",
  "updated": "2023-12-15T15:20:01.000Z",
  "title": "A note on Hamilton decompositions of even-regular multigraphs",
  "authors": [
    "Vincent Pfenninger"
  ],
  "comment": "6 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "In this note, we prove that every even regular multigraph on $n$ vertices with multiplicity at most $r$ and minimum degree at least $rn/2 + o(n)$ has a Hamilton decomposition. This generalises a result of Vaughan who proved an asymptotic version of the multigraph $1$-factorisation conjecture. We derive our result by proving a more general result which states that dense regular multidigraphs that are robust outexpanders have a Hamilton decomposition. This in turn is derived from the corresponding result of K\\\"uhn and Osthus about simple digraphs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-12-15T15:20:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C45",
      "05C35",
      "05C70",
      "05C20",
      "05C38"
    ],
    "keywords": [
      "hamilton decomposition",
      "even-regular multigraphs",
      "dense regular multidigraphs",
      "general result",
      "asymptotic version"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}