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Computing the girth of a planar graph

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Abstract

The girth of a graph G has been defined as the length of a shortest cycle of G. We design an O(n(5/4) log n) algorithm for finding the girth of an undirected n-vertex planar graph, giving the first o(n(2)) algorithm for this problem. Our approach combines several techniques such as graph separation, hammock decomposition, covering of a planar graph with graphs of small tree-width, and dynamic shortest path computation. We discuss extensions and generalizations of our result

Topics: QA76
Publisher: SPRINGER-VERLAG BERLIN
OAI identifier: oai:wrap.warwick.ac.uk:12898
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