In: Theoretical computer science, 2018, vol. 746, p. 49-72
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...
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In: Discrete Mathematics, 2009, vol. 309, p. 4306-4314
Given an undirected graph G=(V,E) with matching number \nu(G), we define d- blockers as subsets of edges B such that \nu(G=(V,E\B))\leq \nu(G)-d. We define d- transversals T as subsets of edges such that every maximum matching M has |M\cap T|\geq d. We explore connections between d-blockers and d-transversals. Special classes of graphs are examined which include complete graphs, regular...
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