Computing the girth of a planar graph in linear time

Authors:
Hsien-Chih Chang;Hsueh-I Lu
Affiliations:
Department of Computer Science and Information Engineering, National Taiwan University;Department of Computer Science and Information Engineering, National Taiwan University
Venue:
COCOON'11 Proceedings of the 17th annual international conference on Computing and combinatorics
Year:
2011

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Abstract

The 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(n5/4 log n) time. Chalermsook, Fakcharoenphol, and Nanongkai reduced the running time to O(n log2 n). Weimann and Yuster further reduced the running time to O(n log n). In this paper, we solve the problem in O(n) time.