{
  "id": "1305.2516",
  "version": "v1",
  "published": "2013-05-11T15:14:26.000Z",
  "updated": "2013-05-11T15:14:26.000Z",
  "title": "On the KŁR conjecture in random graphs",
  "authors": [
    "D. Conlon",
    "W. T. Gowers",
    "W. Samotij",
    "M. Schacht"
  ],
  "comment": "33 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "The K{\\L}R conjecture of Kohayakawa, {\\L}uczak, and R\\\"odl is a statement that allows one to prove that asymptotically almost surely all subgraphs of the random graph G_{n,p}, for sufficiently large p : = p(n), satisfy an embedding lemma which complements the sparse regularity lemma of Kohayakawa and R\\\"odl. We prove a variant of this conjecture which is sufficient for most known applications to random graphs. In particular, our result implies a number of recent probabilistic versions, due to Conlon, Gowers, and Schacht, of classical extremal combinatorial theorems. We also discuss several further applications.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-05-11T15:14:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "random graph",
      "kłr conjecture",
      "sparse regularity lemma",
      "classical extremal combinatorial theorems",
      "kohayakawa"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1305.2516C"
    }
  }
}