Weak saturation stability

Abstract

We study wsat(G, H), the minimum number of edges in a weakly H-saturated subgraph of G. We prove that wsat(Kn, H) is stable (remains the same after independent removal of every edge of Kn with constant probability) for all pattern graphs H such that there exists a 'local' set of edges that percolates in Kn (this is true, for example, for Ks, Ks,s and Ks,s+1). Also, we find a threshold probability for the weak K1,t-saturation stability.