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.
This work was partially supported by the EPA grant R82-5207-01-0, EPSRC grant GR/M60750, and RTDF grant 98/99-0140.
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Djidjev, H.N. (2000). Computing the Girth of a Planar Graph. In: Montanari, U., Rolim, J.D.P., Welzl, E. (eds) Automata, Languages and Programming. ICALP 2000. Lecture Notes in Computer Science, vol 1853. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45022-X_69
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DOI: https://doi.org/10.1007/3-540-45022-X_69
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