{
  "id": "1609.08730",
  "version": "v1",
  "published": "2016-09-28T02:07:12.000Z",
  "updated": "2016-09-28T02:07:12.000Z",
  "title": "Spanning trails with maximum degree at most 4 in $2K_2$-free graphs",
  "authors": [
    "Guantao Chen",
    "M. N. Ellingham",
    "Akira Saito",
    "Songling Shan"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "A graph is called $2K_2$-free if it does not contain two independent edges as an induced subgraph. Mou and Pasechnik conjectured that every $\\frac{3}{2}$-tough $2K_2$-free graph with at least three vertices has a spanning trail with maximum degree at most $4$. In this paper, we confirm this conjecture. We also provide examples for all $t < \\frac{5}{4}$ of $t$-tough graphs that do not have a spanning trail with maximum degree at most $4$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-09-28T02:07:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "maximum degree",
      "spanning trail",
      "free graph",
      "tough graphs",
      "independent edges"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}