Blocking Pairs of Polyhedra Arising from Network Flows

A study is made of blocking pairs of polyhedra (blocking pairs of matrices) that arise in (or can be transformed into) a network flow context. For example, the blocking polyhedron of the polyhedron generated by all integral feasible flows in a capacity-constrained supply-demand network (where all the data are integral) is explicitly determined, and a simple algorithm is described for solving the associated integral packing problem. Applications of these results to k-ways in directed graphs, to (0, 1)-matrices with prescribed row and column sums, and to flow arborescences are described.