Computing the Girth of a Planar Graph (2000)
| Venue: | In Proc. 27th International Colloquium on Automata, Languages and Programming ICALP 2000, volume 1853 of LNCS |
| Citations: | 4 - 0 self |
BibTeX
@INPROCEEDINGS{Djidjev00computingthe,
author = {Hristo N. Djidjev},
title = {Computing the Girth of a Planar Graph},
booktitle = {In Proc. 27th International Colloquium on Automata, Languages and Programming ICALP 2000, volume 1853 of LNCS},
year = {2000},
pages = {821--831},
publisher = {Springer-Verlag}
}
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Abstract
The girth of a graph G has been de ned 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.
