{
  "id": "1306.0461",
  "version": "v1",
  "published": "2013-06-03T15:37:09.000Z",
  "updated": "2013-06-03T15:37:09.000Z",
  "title": "The Ramsey number of the clique and the hypercube",
  "authors": [
    "Gonzalo Fiz Pontiveros",
    "Simon Griffiths",
    "Robert Morris",
    "David Saxton",
    "Jozef Skokan"
  ],
  "comment": "27 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "The Ramsey number r(K_s,Q_n) is the smallest positive integer N such that every red-blue colouring of the edges of the complete graph K_N on N vertices contains either a red n-dimensional hypercube, or a blue clique on s vertices. Answering a question of Burr and Erd\\H{o}s from 1983, and improving on recent results of Conlon, Fox, Lee and Sudakov, and of the current authors, we show that r(K_s,Q_n) = (s-1) (2^n - 1) + 1 for every s \\in \\N and every sufficiently large n \\in \\N.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-06-03T15:37:09.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "ramsey number",
      "complete graph",
      "current authors",
      "vertices contains",
      "smallest positive integer"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1306.0461F"
    }
  }
}