Israel Journal of Mathematics

, Volume 197, Issue 1, pp 199–214 | Cite as

Turán numbers for Ks,t-free graphs: Topological obstructions and algebraic constructions

  • Pavle V. M. Blagojević
  • Boris Bukh
  • Roman Karasev
Article

Abstract

We show that every hypersurface in ℝs × ℝs contains a large grid, i.e., the set of the form S × T, with S, T ⊂ ℝs. We use this to deduce that the known constructions of extremal K2,2-free and K3,3-free graphs cannot be generalized to a similar construction of Ks,s-free graphs for any s ≥ 4. We also give new constructions of extremal Ks,t-free graphs for large t.

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Copyright information

© Hebrew University Magnes Press 2013

Authors and Affiliations

  • Pavle V. M. Blagojević
    • 1
    • 2
  • Boris Bukh
    • 3
  • Roman Karasev
    • 4
    • 5
  1. 1.Mathematički Institut SANUBeogradSerbia
  2. 2.Institut für Mathematik FreieUniversitt BerlinBerlinGermany
  3. 3.Department of Mathematical SciencesCarnegie Mellon UniversityPittsburghUSA
  4. 4.Department of MathematicsMoscow Institute of Physics and TechnologyDolgoprudnyRussia
  5. 5.Laboratory of Discrete and Computational GeometryYaroslavl’ State UniversityYaroslavl’Russia

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