A separator theorem for graphs of bounded genus
Journal of Algorithms
Pfaffian orientations 0-1 permanents, and even cycles in directed graphs
Discrete Applied Mathematics - Combinatorics and complexity
Planar graph decomposition and all pairs shortest paths
Journal of the ACM (JACM)
Approximation algorithms for NP-complete problems on planar graphs
Journal of the ACM (JACM)
Faster shortest-path algorithms for planar graphs
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Journal of the ACM (JACM)
Subgraph isomorphism in planar graphs and related problems
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Computing the Girth of a Planar Graph in O(n logn) Time
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Computing the Girth of a Planar Graph in $O(n \logn)$ Time
SIAM Journal on Discrete Mathematics
| Hi-index | 0.00 |
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.