{
  "id": "2106.00904",
  "version": "v1",
  "published": "2021-06-02T02:48:51.000Z",
  "updated": "2021-06-02T02:48:51.000Z",
  "title": "The maximum size of a nonhamiltonian graph with given order and connectivity",
  "authors": [
    "Xingzhi Zhan",
    "Leilei Zhang"
  ],
  "comment": "12 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Motivated by work of Erd\\H{o}s, Ota determined the maximum size $g(n,k)$ of a $k$-connected nonhamiltonian graph of order $n$ in 1995. But for some pairs $n,k,$ the maximum size is not attained by a graph of connectivity $k.$ For example, $g(15,3)=77$ is attained by a unique graph of connectivity $7,$ not $3.$ In this paper we obtain more precise information by determining the maximum size of a nonhamiltonian graph of order $n$ and connectivity $k,$ and determining the extremal graphs. Consequently we solve the corresponding problem for nontraceable graphs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-06-02T02:48:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "maximum size",
      "connectivity",
      "connected nonhamiltonian graph",
      "unique graph",
      "precise information"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}