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

@article{Blagojevic2013TurnNF,
  title={Tur{\'a}n numbers for Ks,t-free graphs: Topological obstructions and algebraic constructions},
  author={Pavle V. M. Blagojevic and Boris Bukh and Roman N. Karasev},
  journal={Israel Journal of Mathematics},
  year={2013},
  volume={197},
  pages={199-214}
}
  • Pavle V. M. Blagojevic, Boris Bukh, Roman N. Karasev
  • Published 2013
  • Mathematics
  • Israel Journal of Mathematics
  • 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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