Israel Journal of Mathematics

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

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

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


We show that every hypersurface in ℝ s × ℝ s contains a large grid, i.e., the set of the form S × T, with S, T ⊂ 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 ≥ 4. We also give new constructions of extremal K s,t -free graphs for large t.


Spectral Sequence Generic Polynomial Cohomology Ring Euler Class Algebraic Construction 
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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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