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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