{
  "id": "2110.01897",
  "version": "v2",
  "published": "2021-10-05T09:32:42.000Z",
  "updated": "2023-04-23T12:07:48.000Z",
  "title": "The size-Ramsey number of cubic graphs",
  "authors": [
    "David Conlon",
    "Rajko Nenadov",
    "Miloš Trujić"
  ],
  "comment": "15 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "We show that the size-Ramsey number of any cubic graph with $n$ vertices is $O(n^{8/5})$, improving a bound of $n^{5/3 + o(1)}$ due to Kohayakawa, R\\\"{o}dl, Schacht, and Szemer\\'{e}di. The heart of the argument is to show that there is a constant $C$ such that a random graph with $C n$ vertices where every edge is chosen independently with probability $p \\geq C n^{-2/5}$ is with high probability Ramsey for any cubic graph with $n$ vertices. This latter result is best possible up to the constant.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2023-04-23T12:07:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "cubic graph",
      "size-ramsey number",
      "high probability ramsey",
      "random graph",
      "kohayakawa"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}