{
  "id": "2012.00988",
  "version": "v1",
  "published": "2020-12-02T06:36:44.000Z",
  "updated": "2020-12-02T06:36:44.000Z",
  "title": "Hamilton decompositions of line graphs",
  "authors": [
    "Darryn Bryant",
    "Sara Herke",
    "Barbara Maenhaut",
    "Benjamin R. Smith"
  ],
  "comment": "106 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "It is proved that if a graph is regular of even degree and contains a Hamilton cycle, or regular of odd degree and contains a Hamiltonian $3$-factor, then its line graph is Hamilton decomposable. This result partially extends Kotzig's result that a $3$-regular graph is Hamiltonian if and only if its line graph is Hamilton decomposable, and proves the conjecture of Bermond that the line graph of a Hamilton decomposable graph is Hamilton decomposable.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-12-02T06:36:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C70",
      "05C51"
    ],
    "keywords": [
      "line graph",
      "hamilton decompositions",
      "result partially extends kotzigs result",
      "hamilton cycle",
      "hamilton decomposable graph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 106,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}