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

Abstract : We study the following problem: for given integers d,k and graph G,can we reduce some fixed graph parameter π of Gby 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 wechoose 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
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Öznur Yaşar Diner, Daniël Paulusma, Christophe Picouleau, Bernard Ries. Contraction and deletion blockers for perfect graphs and H-free graphs. Theoretical Computer Science, Elsevier, 2018, 746, pp.49-72. ⟨10.1016/j.tcs.2018.06.023⟩. ⟨hal-02436808⟩

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