{
  "id": "2002.01297",
  "version": "v1",
  "published": "2020-02-04T14:24:55.000Z",
  "updated": "2020-02-04T14:24:55.000Z",
  "title": "Induced Ramsey number for a star versus a fixed graph",
  "authors": [
    "Maria Axenovich",
    "Izolda Gorgol"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "For graphs G and H, let the induced Ramsey number IR(H,G) be the smallest number of vertices in a graph F such that any coloring of the edges of F in red and blue, there is either a red induced copy of H or a blue induced copy of G. In this note we consider the case when G=Sn is a star on n edges, for large n, and H is a fixed graph. We prove that (r-1)n < IR(H, Sn) < (r-1)(r-1)n + cn, for any c>0, sufficiently large n, and r denoting the chromatic number of H. The lower bound is asymptotically tight for any fixed bipartite H. The upper bound is attained up to a constant factor, for example by a clique H.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-02-04T14:24:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fixed graph",
      "induced ramsey number ir",
      "constant factor",
      "upper bound",
      "smallest number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}