Blockers and transversals in some subclasses of bipartite graphs: When caterpillars are dancing on a grid

AbstractGiven an undirected graph G=(V,E) with matching number ν(G), a d-blocker is a subset of edges B such that ν((V,E∖B))≤ν(G)−d and a d-transversal T is a subset of edges such that every maximum matching M has |M∩T|≥d. While the associated decision problem is NP-complete in bipartite graphs we show how to construct efficiently minimum d-transversals and minimum d-blockers in the special cases where G is a grid graph or a tree