Department of Computer Science | Institute of Theoretical Computer Science | CADMO

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar Talk Information |

**Date and Time**: Thursday, August 11, 2005, 12:15 pm

**Duration**: This information is not available in the database

**Location**: This information is not available in the database

**Speaker**: Martin Marciniszyn

We prove the existence of many complete graphs in almost all sufficiently
dense partitions obtained by an application of Szemerédi's Regularity Lemma.
More precisely, we consider the number of complete graphs K_{l} on l vertices
in l-partite graphs where each partition class consists of n vertices and
there is an ε-regular graph on m edges between any two partition
classes. We show that for all β >0, at most a β^{m}-fraction of graphs
in this family contain less than the expected number of copies of K_{l}
provided ε is sufficiently small and m >= Cn^{2-1/(l-1)} for a constant C > 0 and n sufficiently large. This result is a counting version
of a restricted version of a conjecture by Kohayakawa, Luczak, and Rödl (1997) and has several implications for random graphs.

This is joint work with Stefanie Gerke and Angelika Steger.

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