{
  "id": "2411.19197",
  "version": "v1",
  "published": "2024-11-28T15:11:38.000Z",
  "updated": "2024-11-28T15:11:38.000Z",
  "title": "Balanced 1-Factorisations of 3- and 4-Regular Circulant Graphs",
  "authors": [
    "Jeremy Mitchell"
  ],
  "comment": "27 pages, 11 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "We investigate 1-factorisations in which the 2-regular graphs that occur as the union of a pair of 1-factors appear an equal number of times across the unions of all pairs of 1-factors in the 1-factorisation. We call such 1-factorisations balanced 1-factorisations (B1Fs) and we present some results on B1Fs of 3- and 4-regular circulant graphs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-11-28T15:11:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C70"
    ],
    "keywords": [
      "circulant graphs",
      "equal number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}