{
  "id": "0711.4394",
  "version": "v2",
  "published": "2007-11-28T01:00:01.000Z",
  "updated": "2007-11-30T15:13:36.000Z",
  "title": "A note on a degree sum condition for long cycles in graphs",
  "authors": [
    "Janusz Adamus"
  ],
  "comment": "5 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "We conjecture that a 2-connected graph $G$ of order $n$, in which $d(x)+d(y)\\geq n-k$ for every pair of non-adjacent vertices $x$ and $y$, contains a cycle of length $n-k$ ($k<n/2$), unless $G$ is bipartite and $n-k$ is odd. This generalizes to long cycles a well-known degree sum condition for hamiltonicity of Ore. The conjecture is shown to hold for $k=1$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-11-30T15:13:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C38"
    ],
    "keywords": [
      "long cycles",
      "well-known degree sum condition",
      "conjecture",
      "non-adjacent vertices",
      "generalizes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0711.4394A"
    }
  }
}