Blockers and transversals

Given G = (V,E) an undirected graph with matching number ν(G), we define d-blockers as subsets of edges B such that ν(G′ = (V,E \B)) ≤ ν(G)−d. We define d-transversals T as subsets of edges such that every maximum matchingM has |M ∩T | ≥ d. We explore connections between d-blockers and d-transversals. Special classes of graphs are examined which include complete graphs, regular bipartite graphs, chains and cycles and we construct minimum d-transversals and d-blockers in these special graphs. We also study the complexity status of finding minimum transversals and blockers in arbitrary graphs.