We show a fast algorithm for determining the set of relevant edges in a
planar undirected unweighted graph with respect to the maximum flow. This is a
special case of the \emph{max flow vitality} problem, that has been efficiently
solved for general undirected graphs and st-planar graphs. The
\emph{vitality} of an edge of a graph with respect to the maximum flow between
two fixed vertices s and t is defined as the reduction of the maximum flow
caused by the removal of that edge. In this paper we show that the set of edges
having vitality greater than zero in a planar undirected unweighted graph with
n vertices, can be found in O(nlogn) worst-case time and O(n) space.Comment: 9 pages, 4 figure