## 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, November 26, 2015, 12:15 pm

Duration: 30 minutes

Location: CAB G51

Speaker: Dániel Korándi

## Saturation in random graphs

A graph $H$ is $K_s$-saturated if it is a maximal $K_s$-free graph, i.e., $H$ contains no clique on $s$ vertices, but the addition of any missing edge creates one. The minimum number of edges in a $K_s$-saturated graph was determined over 50 years ago by Zykov and independently by Erdős, Hajnal and Moon. In this talk, we consider the random analog of this problem: minimizing the number of edges in a maximal $K_s$-free subgraph of the Erdős-Rényi random graph $G(n,p)$. We give asymptotically tight estimates on this minimum, and also provide exact bounds for the related notion of weak saturation in random graphs.

Joint work with Benny Sudakov.

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