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 5/4logn) 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.
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Chang, HC., Lu, HI. (2011). Computing the Girth of a Planar Graph in Linear Time. In: Fu, B., Du, DZ. (eds) Computing and Combinatorics. COCOON 2011. Lecture Notes in Computer Science, vol 6842. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22685-4_20
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DOI: https://doi.org/10.1007/978-3-642-22685-4_20
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