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The vitality of an edge in a graph with respect to the maximum flow betweentwo fixed vertices $s$ and $t$ is defined as the reduction of the maximum flowvalue caused by the removal of that edge.  The max-flow vitality problem has already been efficiently solved for$st$-planar graphs but has remained open for general planar graphs. For thefirst time our result provides an optimal solution for general planar graphsalthough restricted to the case of unweighted planar graphs.

A Linear Time Algorithm for Computing Max-Flow Vitality in Undirected Unweighted Planar Graphs