Threshold for stability of weak saturation

Abstract

AbstractWe study the weak ‐saturation number of the Erdős–Rényi random graph , denoted by , where is the complete graph on vertices. In 2017, Korándi and Sudakov proved that the weak ‐saturation number of is stable, in the sense that it remains the same after removing edges with constant probability. In this paper, we prove that there exists a threshold for this stability property and give upper and lower bounds on the threshold. This generalizes the result of Korándi and Sudakov. A general upper bound on is also provided.