Blockers and transversals

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