{
  "id": "1710.06037",
  "version": "v1",
  "published": "2017-10-17T00:27:14.000Z",
  "updated": "2017-10-17T00:27:14.000Z",
  "title": "On Hamilton Decompositions of Line Graphs of Non-Hamiltonian Graphs and Graphs without Separating Transitions",
  "authors": [
    "Darryn Bryant",
    "Barbara Maenhaut",
    "Benjamin R. Smith"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "In contrast with Kotzig's result that the line graph of a $3$-regular graph $X$ is Hamilton decomposable if and only if $X$ is Hamiltonian, we show that for each integer $k\\geq 4$ there exists a simple non-Hamiltonian $k$-regular graph whose line graph has a Hamilton decomposition. We also answer a question of Jackson by showing that for each integer $k\\geq 3$ there exists a simple connected $k$-regular graph with no separating transitions whose line graph has no Hamilton decomposition.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-10-17T00:27:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C45",
      "05C51",
      "05C70"
    ],
    "keywords": [
      "line graph",
      "hamilton decomposition",
      "separating transitions",
      "non-hamiltonian graphs",
      "regular graph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}