{
  "id": "1404.0496",
  "version": "v2",
  "published": "2014-04-02T09:17:57.000Z",
  "updated": "2014-07-18T11:20:41.000Z",
  "title": "A Common Generalization of Dirac's two Theorems",
  "authors": [
    "Zh. G. Nikoghosyan"
  ],
  "comment": "7 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $G$ be a 2-connected graph of order $n$ and let $c$ be the circumference - the order of a longest cycle in $G$. In this paper we present a sharp lower bound for the circumference based on minimum degree $\\delta$ and $p$ - the order of a longest path in $G$. This is a common generalization of two earlier classical results for 2-connected graphs due to Dirac: (i) $c\\ge \\min\\{n,2\\delta\\}$; and (ii) $c\\ge\\sqrt{2p}$. Moreover, the result is stronger than (ii).",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-07-18T11:20:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "common generalization",
      "sharp lower bound",
      "longest cycle",
      "circumference",
      "minimum degree"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1404.0496N"
    }
  }
}