Authors: Blagojević, Pavle 
Bukh, Boris
Karasev, Roman
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Turán numbers for Ks,t-free graphs: Topological obstructions and algebraic constructions
Journal: Israel Journal of Mathematics
Volume: 197
Issue: 1
First page: 199
Last page: 214
Issue Date: 1-Oct-2013
Rank: M22
ISSN: 0021-2172
DOI: 10.1007/s11856-012-0184-z
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 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.
Publisher: Springer Link
Project: European Union’s Seventh Framework Programme (FP7/2007-2013) / ERC, Grant agreement no. 247029-SDModels
Advanced Techniques of Cryptology, Image Processing and Computational Topology for Information Security 
President’s of Russian Federation, grant MD-352.2012.1
Russian Foundation for Basic Research, grants 10-01-00096 and 10-01-00139
Russian government, project 11.G34.31.0053

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