Contraction and Deletion Blockers for Perfect Graphs and H -free Graphs - Diner, Ö.Y.; Paulusma, D.; Picouleau, C.; Ries, B. (Theoretical Computer Science, 2018)
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}S={ec} and S={vd}S={vd} and π∈{χ,ω,α}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}S={ec} and S={vd}S={vd} and π∈{χ,ω,α}π∈{χ,ω,α} restricted to H-free graphs.
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