## Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

# Mittagsseminar (in cooperation with M. Ghaffari, A. Steger and B. Sudakov)

 Mittagsseminar Talk Information

Date and Time: Thursday, October 10, 2013, 12:15 pm

Duration: 30 minutes

Location: CAB G51

Speaker: Andreas Noever

## A mixed density embedding lemma

The KŁR conjecture (an embedding lemma for sparse regular graphs) was proved last year independently by Balogh, Morris, Samotij and Saxton, Thomason. The main tool used during the proof is a powerful container theorem for independent sets in hypergraphs. In this talk we present the proof of the KŁR conjecture based on these container theorems. We also show that with only slight modifications one obtains a generalised embedding lemma which allows one to put additional restrictions on the embedded graph F. For example we can require that F induces a triangle in some other fixed graph.

Information for students and suggested topics for student talks