How Vulnerable is an Undirected Planar Graph with Respect to Max Flow

Lorenzo Balzotti, Paolo Giulio Franciosa

Abstract: We study the problem of computing the vitality of edges and vertices with respect to the st-max flow in undirected planar graphs, where the vitality of an edge/vertex is the st-max flow decrease when the edge/vertex is removed from the graph. This allows us to establish the vulnerability of the graph with respect to the st-max flow.