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arXiv · 1104.4892

Computing the Girth of a Planar Graph in Linear Time

Hsien-Chih Chang·Hsueh-I Lu
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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(n^{5/4} log n) time. Chalermsook, Fakcharoenphol, and Nanongkai reduced the running time to O(n log^2 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.

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Hsien-Chih Chang, Hsueh-I Lu. 2011-04-26. Computing the Girth of a Planar Graph in Linear Time. https://doi.org/10.1137/110832033

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