Abstract

AbstractThe girth of a graph is the minimum weight of all simple cycles of the graph. We study the problem of determining the girth of an n-node unweighted undirected planar graph. The first non-trivial algorithm for the problem, given by Djidjev, runs in O(n 5/4logn) time. Chalermsook, Fakcharoenphol, and Nanongkai reduced the running time to O(nlog2 n). Weimann and Yuster further reduced the running time to O(nlogn). In this paper, we solve the problem in O(n) time.KeywordsPlanar GraphChromatic NumberDecomposition TreeSimple CycleDistance QueryThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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