{
  "id": "1308.3144",
  "version": "v2",
  "published": "2013-08-14T14:51:55.000Z",
  "updated": "2014-05-24T11:42:10.000Z",
  "title": "Long cycles in random subgraphs of graphs with large minimum degree",
  "authors": [
    "Oliver Riordan"
  ],
  "comment": "4 pages, 1 figure; figure reoriented",
  "categories": [
    "math.CO",
    "math.PR"
  ],
  "abstract": "Let $G$ be any graph of minimum degree at least $k$, and let $G_p$ be the random subgraph of $G$ obtained by keeping each edge independently with probability $p$. Recently, Krivelevich, Lee and Sudakov showed that if $pk\\to\\infty$ then with probability tending to 1 $G_p$ contains a cycle of length at least $(1-o(1))k$. We give a much shorter proof of this result, also based on depth-first search.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-05-24T11:42:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C80"
    ],
    "keywords": [
      "large minimum degree",
      "random subgraph",
      "long cycles",
      "probability",
      "shorter proof"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1308.3144R"
    }
  }
}