{
  "id": "1906.06915",
  "version": "v1",
  "published": "2019-06-17T09:32:02.000Z",
  "updated": "2019-06-17T09:32:02.000Z",
  "title": "On the size-Ramsey number of grid graphs",
  "authors": [
    "Dennis Clemens",
    "Meysam Miralaei",
    "Damian Reding",
    "Mathias Schacht",
    "Anusch Taraz"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "The size-Ramsey number of a graph $F$ is the smallest number of edges in a graph $G$ with the Ramsey property for $F$, that is, with the property that any 2-colouring of the edges of $G$ contains a monochromatic copy of $F$. We prove that the size-Ramsey number of the grid graph on $n\\times n$ vertices is bounded from above by $n^{3+o(1)}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-17T09:32:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05D10"
    ],
    "keywords": [
      "size-ramsey number",
      "grid graph",
      "smallest number",
      "ramsey property"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}