{
  "id": "0907.2657",
  "version": "v1",
  "published": "2009-07-15T17:10:01.000Z",
  "updated": "2009-07-15T17:10:01.000Z",
  "title": "The Ramsey number of dense graphs",
  "authors": [
    "David Conlon"
  ],
  "comment": "15 pages",
  "doi": "10.1112/blms/bds097",
  "categories": [
    "math.CO"
  ],
  "abstract": "The Ramsey number r(H) of a graph H is the smallest number n such that, in any two-colouring of the edges of K_n, there is a monochromatic copy of H. We study the Ramsey number of graphs H with t vertices and density \\r, proving that r(H) \\leq 2^{c \\sqrt{\\r} \\log (2/\\r) t}. We also investigate some related problems, such as the Ramsey number of graphs with t vertices and maximum degree \\r t and the Ramsey number of random graphs in \\mathcal{G}(t, \\r), that is, graphs on t vertices where each edge has been chosen independently with probability \\r.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-07-15T17:10:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C55"
    ],
    "keywords": [
      "ramsey number",
      "dense graphs",
      "smallest number",
      "monochromatic copy",
      "maximum degree"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0907.2657C"
    }
  }
}