Finding small simple cycle separators for 2-connected planar graphs

Abstract

We show that every 2-connected triangulated planar graph with n vertices has a simple cycle C of length at most 2√2 · n which separates the interior vertices A from the exterior vertices B such that neither A nor B contain more than 2 3n vertices. The method also gives a linear time sequential algorithm for finding this simple cycle and an NC parallel algorithm. In general, if the maximum face size is d then we exhibit a cycle C as above of size at most 2√ d · n.