Turán numbers for K s,t -free graphs: Topological obstructions and algebraic constructions
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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.
KeywordsSpectral Sequence Generic Polynomial Cohomology Ring Euler Class Algebraic Construction
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