Affiliation:
1. Los Alamos National Laboratory, Los Alamos, NM
Abstract
The
girth
of a graph
G
is the length of a shortest cycle of
G
. In this article we design an
O
(
n
5/4
log
n
) algorithm for finding the girth of an undirected
n
-vertex planar graph, the first
o
(
n
2
) algorithm for this problem. We also extend our results for the class of graphs embedded into an orientable surface of small genus. Our approach uses several techniques such as graph partitioning, hammock decomposition, graph covering, and dynamic shortest-path computation. We discuss extensions and generalizations of our result.
Funder
U.S. Department of Energy
Engineering and Physical Sciences Research Council
RTDF
Environmental Protection Agency
Publisher
Association for Computing Machinery (ACM)
Subject
Mathematics (miscellaneous)
Reference31 articles.
1. Aho A. V. Hopcroft J. E. and Ullman J. D. 1974. The Design and Analysis of Computer Algorithms. Addison-Wesley Reading MA. Aho A. V. Hopcroft J. E. and Ullman J. D. 1974. The Design and Analysis of Computer Algorithms. Addison-Wesley Reading MA.
2. Color-coding
3. Finding and counting given length cycles
4. Approximation algorithms for NP-complete problems on planar graphs
5. Chromatic number, girth and maximal degree
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