H-percolation with a random H
In H-percolation, we start with a random graph G(n,p) and then iteratively add edges that complete copies of H. The process percolates if all edges missing from G(n,p) are eventually added. We find the critical percolation threshold p_c when H=G(k,1/2) is a uniformly random graph. In this sense, we find p_c for most graphs H. This solves a problem of Balogh, Bollobás and Morris. Joint work with Zsolt Bartha and Gal Kronenberg.