{
  "id": "1302.3840",
  "version": "v1",
  "published": "2013-02-15T18:32:18.000Z",
  "updated": "2013-02-15T18:32:18.000Z",
  "title": "On the Ramsey number of the triangle and the cube",
  "authors": [
    "Gonzalo Fiz Pontiveros",
    "Simon Griffiths",
    "Robert Morris",
    "David Saxton",
    "Jozef Skokan"
  ],
  "comment": "16 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "The Ramsey number r(K_3,Q_n) is the smallest integer N such that every red-blue colouring of the edges of the complete graph K_N contains either a red n-dimensional hypercube, or a blue triangle. Almost thirty years ago, Burr and Erd\\H{o}s conjectured that r(K_3,Q_n) = 2^{n+1} - 1 for every n \\in \\N, but the first non-trivial upper bound was obtained only recently, by Conlon, Fox, Lee and Sudakov, who proved that r(K_3,Q_n) \\le 7000 \\cdot 2^n. Here we show that r(K_3,Q_n) = (1 + o(1)) 2^{n+1} as n \\to \\infty.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-02-15T18:32:18.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "ramsey number",
      "first non-trivial upper bound",
      "blue triangle",
      "complete graph",
      "red n-dimensional hypercube"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1302.3840F"
    }
  }
}