Thresholds for contagious sets in random graphs

Bootstrap percolation with threshold r on a graph G evolves as follows: initially some of its vertices are infected, and then any vertex with at least r infected neighbors becomes infected. On the Erdos-Renyi graph G(n,p) we identify the sharp threshold for p above which there is with high probability a set of size r whose infection results in the entire infection of the graph. Joint work with Omer Angel.