## 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: Tuesday, October 21, 2014, 12:15 pm

Duration: 30 minutes

Location: CAB G51

Speaker: Michael Krivelevich (Tel Aviv University)

## Contagious sets in random graphs

Consider the following activation process in graphs: a vertex is active either if it belongs to a set of initially activated vertices, or at some point it has at least 2 active neighbors. (In perhaps more commonly used terms, this is the so called bootstrap percolation with a threshold parameter $r=2$.)

A CONTAGIOUS SET in a graph $G$ is a set whose activation results with the entire graph being active. Let $m(G,2)$ be the minimum size of a contagious set in $G$.

Recently, in a joint work with Uriel Feige and Daniel Reichman, we showed that for the binomial random graph $G\sim G(n,p)$, with $p=d/n$ and $1 \ll d \ll n^{1/2}$, the value of the parameter $m(G,2)$ is typically of the asymptotic order $n/(d^2\log d)$.

In this talk I will discuss this result, as well as some prior/relevant papers.

Previous talks by year:   2018  2017  2016  2015  2014  2013  2012  2011  2010  2009  2008  2007  2006  2005  2004  2003  2002  2001  2000  1999  1998  1997  1996

Information for students and suggested topics for student talks