An Optimal Algorithm for Product Structure in Planar Graphs
Abstract
The Product Structure Theorem for planar graphs (Dujmovi\'c et al.\ JACM, 67(4):22) states that any planar graph is contained in the strong product of a planar 3-tree, a path, and a 3-cycle. We give a simple linear-time algorithm for finding this decomposition as well as several related decompositions. This improves on the previous O(n n) time algorithm (Morin.\ Algorithmica, 85(5):1544--1558).
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