{
  "id": "2203.02653",
  "version": "v1",
  "published": "2022-03-05T04:35:50.000Z",
  "updated": "2022-03-05T04:35:50.000Z",
  "title": "Estimating the circumference of a graph in terms of its leaf number",
  "authors": [
    "Jingru Yan"
  ],
  "comment": "14 pages, 9 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $\\mathcal{T}$ be the set of spanning trees of $G$ and let $L(T)$ be the number of leaves in a tree $T$. The leaf number $L(G)$ of $G$ is defined as $L(G)=\\max\\{L(T)|T\\in \\mathcal{T}\\}$. Let $G$ be a connected graph of order $n$ and minimum degree $\\delta$ such that $L(G)\\leq 2\\delta-1$. We show that the circumference of $G$ is at least $n-1$, and that if $G$ is regular then $G$ is hamiltonian.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-03-05T04:35:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C38",
      "05C45"
    ],
    "keywords": [
      "leaf number",
      "circumference",
      "estimating",
      "minimum degree"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}