Blockers for the Stability Number and the Chromatic Number

Given an undirected graph G = (V, E) and two positive integers k and d, we are interested in finding a set of edges (resp. non-edges) of size at most k to delete (resp. to add) in such a way that the chromatic number (resp. stability number) in the resulting graph will decrease by at least d compared to the original graph. We investigate these two problems in various classes of graphs (split graphs, threshold graphs, bipartite graphs and their complements) and determine their computational complexity. In some of the polynomial-time solvable cases, we also give a structural description of a solution.