Affiliation:
1. School of Mathematics Institute for Research in Fundamental Sciences (IPM) Tehran Iran
2. School of Mathematical Sciences Anhui University Hefei Anhui China
3. Department of Computer Science University of Sheffield Sheffield UK
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.
Funder
Iran National Science Foundation
National Natural Science Foundation of China
Natural Science Foundation of Anhui Province