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# Turán numbers for K(s,t)-free graphs: topological obstructions and algebraic constructions

## Pavle Blagojević, Boris Bukh, Roman Karasev – 2011

Focus Area 3: Topological connectivity and diameter of Discrete Structures We show that every hypersurface in $\R^s\times \R^s$ contains a large grid, i.e., the set of the form $S\times T$, with $S,T\subset \R^s$. 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 $s\geq 4$. We also give new constructions of extremal $K_{s,t}$-free graphs for large $t$.

Title
Turán numbers for K(s,t)-free graphs: topological obstructions and algebraic constructions (extended abstract)
Author
Pavle Blagojević, Boris Bukh, Roman Karasev
Date
2011
Appeared in
Electronic Notes in Discrete Mathematics 38 (2011) 141-145, The Sixth European Conference on Combinatorics, Graph Theory and Applications, EuroComb 2011
Type
Text