{
  "id": "2110.01281",
  "version": "v6",
  "published": "2021-10-04T09:45:03.000Z",
  "updated": "2022-08-23T07:57:02.000Z",
  "title": "Forbidden subgraphs and 2-factors in 3/2-tough graphs",
  "authors": [
    "Masahiro Sanka"
  ],
  "comment": "16 pages, 3 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "A graph $G$ is $H$-free if it has no induced subgraph isomorphic to $H$, where $H$ is a graph. In this paper, we show that every $\\frac{3}{2}$-tough $(P_4 \\cup P_{10})$-free graph has a 2-factor. The toughness condition of this result is sharp. Moreover, for any $\\varepsilon>0$ there exists a $(2-\\varepsilon)$-tough $2P_5$-free graph without a 2-factor. This implies that the graph $P_4 \\cup P_{10}$ is best possible for a forbidden subgraph in a sense.",
  "revisions": [
    {
      "version": "v6",
      "updated": "2022-08-23T07:57:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C38",
      "05C42",
      "05C45"
    ],
    "keywords": [
      "forbidden subgraph",
      "free graph",
      "toughness condition",
      "induced subgraph isomorphic"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}