Weak saturation stability

The paper studies wsat(G,H) which is 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 percolating in Kn. This is true, for example, for cliques and complete bipartite graphs. We also find a threshold probability for the weak K1,t-saturation stability