Probability threshold for the stability of $\alpha (G(n,r,s))$

Abstract

Let $G(n,r,s)$ be a graph $(V,E)$ such that $V=\left(\genfrac{}{}{0ex}{}{[n]}{r}\right)$ and $E=\{(u,v)||u\cap v|=s\}.$In this paper we study the probability threshold for the exact stability of the independence number of $G(n,r,s)$ where $r>2s+2$. We improve the previous result of Pyaderkin that implied asymptotic stability of the independence number.