A Separator Theorem for Graphs of Bounded Genus
A Separator Theorem for Graphs of Bounded Genus
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We show that every 2-connected triangulated planar graph with n vertices has a simple cycle C of length at most 4@@@@n which separates the interior vertices A from the exterior vertices B such that neither A nor B contains more than 2/3n vertices. The method also gives a linear time algorithm for finding the simple cycle. In general, if the maximum face size is d then we exhibit a cycle C as above of size at most 2@@@@2d•n.