Turán numbers for K(s,t)-free graphs: topological obstructions and algebraic constructions
Pavle Blagojević, Boris Bukh, Roman Karasev – 2013
Focus Area 3: Topological connectivity and diameter of Discrete Structures 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.