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 the 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.