Asymptotics of the independence number of a random subgraph of the graph $G(n,r,<s)$

In this paper, we deal with a probabilistic version of a classical problem in extremal combinatorics. An extension to the case of nonconstant parameters and to the case of different probabilities of edges is established for a stability theorem asserting that the independence number of a random subgraph of a graph $G(n,r,<s)$ does not change asymptotically, provided that the initial edges are deleted independently.