{
  "id": "2106.07083",
  "version": "v1",
  "published": "2021-06-13T20:23:12.000Z",
  "updated": "2021-06-13T20:23:12.000Z",
  "title": "Hamiltonicity of 3-tough $(K_2 \\cup 3K_1)$-free graphs",
  "authors": [
    "Andrew Hatfield",
    "Elizabeth Grimm"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Chv\\'{a}tal conjectured in 1973 the existence of some constant $t$ such that all $t$-tough graphs with at least three vertices are hamiltonian. While the conjecture has been proven for some special classes of graphs, it remains open in general. We say that a graph is $(K_2 \\cup 3K_1)$-free if it contains no induced subgraph isomorphic to $K_2 \\cup 3K_1$, where $K_2 \\cup 3K_1$ is the disjoint union of an edge and three isolated vertices. In this paper, we show that every 3-tough $(K_2 \\cup 3K_1)$-free graph with at least three vertices is hamiltonian.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-06-13T20:23:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "free graph",
      "hamiltonicity",
      "hamiltonian",
      "special classes",
      "remains open"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}