Contraction and deletion blockers for perfect graphs and H-free graphs

We study the following problem: for given integers d, k and graph G, can we reduce some fixed graph parameter π of G by at least d via at most k graph operations from some fixed set S? As parameters we take the chromatic number χ, clique number ω and independence number α, and as operations we choose edge contraction ec and vertex deletion vd. We determine the complexity of this problem for S={ec} and S={vd} and π∈{χ,ω,α} for a number of subclasses of perfect graphs. We use these results to determine the complexity of the problem for S={ec} and S={vd} and π∈{χ,ω,α} restricted to H-free graphs.