{
  "id": "0711.4999",
  "version": "v1",
  "published": "2007-11-30T18:44:32.000Z",
  "updated": "2007-11-30T18:44:32.000Z",
  "title": "On the Ramsey multiplicity of complete graphs",
  "authors": [
    "David Conlon"
  ],
  "comment": "15 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "We show that, for $n$ large, there must exist at least \\[\\frac{n^t}{C^{(1+o(1))t^2}}\\] monochromatic $K_t$s in any two-colouring of the edges of $K_n$, where $C \\approx 2.18$ is an explicitly defined constant. The old lower bound, due to Erd\\H{o}s \\cite{E62}, and based upon the standard bounds for Ramsey's theorem, is \\[\\frac{n^t}{4^{(1+o(1))t^2}}.\\]",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-11-30T18:44:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C55"
    ],
    "keywords": [
      "complete graphs",
      "ramsey multiplicity",
      "old lower bound",
      "ramseys theorem",
      "standard bounds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0711.4999C"
    }
  }
}