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We show a fast algorithm for determining the set of edges in a planarundirected unweighted graph, whose deletion reduces the maximum flow betweentwo fixed vertices. This is a special case of the max flow vitality problem,that has been efficiently solved for general undirected graphs and st-planargraphs. The vitality of an edge of a graph with respect to the maximum flowbetween two fixed vertices s and t is defined as the reduction of the maximumflow caused by the removal of that edge. In this paper we show that the set ofedges having vitality greater than zero in a planar undirected unweighted graphwith n vertices can be found in O(n log n) worst-case time and O(n) space.

Max-flow vitality in undirected unweighted planar graphs