Computing the Girth of a Planar Graph

The girth of a G has been defined as the length of a shortest cycle of G. We design an O(n5/4log n) algorithm for finding the girth of an undirected n-vertex planar graph, giving the first o(n2) 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.

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