{
  "id": "1108.5254",
  "version": "v3",
  "published": "2011-08-26T08:14:56.000Z",
  "updated": "2012-06-03T10:50:56.000Z",
  "title": "Turán numbers for $K_{s,t}$-free graphs: topological obstructions and algebraic constructions",
  "authors": [
    "Pavle Blagojević",
    "Boris Bukh",
    "Roman Karasev"
  ],
  "comment": "Fixed a small mistake in the application of Proposition 1",
  "journal": "Israel Journal of Mathematics 197:1 (2013), 199-214",
  "doi": "10.1007/s11856-012-0184-z",
  "categories": [
    "math.CO",
    "math.AG",
    "math.AT"
  ],
  "abstract": "We show that every hypersurface in $\\R^s\\times \\R^s$ contains a large grid, i.e., the set of the form $S\\times T$, with $S,T\\subset \\R^s$. We use this to deduce that the known constructions of extremal $K_{2,2}$-free and $K_{3,3}$-free graphs cannot be generalized to a similar construction of $K_{s,s}$-free graphs for any $s\\geq 4$. We also give new constructions of extremal $K_{s,t}$-free graphs for large $t$.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2012-06-03T10:50:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "free graphs",
      "turán numbers",
      "algebraic constructions",
      "topological obstructions",
      "large grid"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1108.5254B"
    }
  }
}