Elsevier

Discrete Applied Mathematics

Volume 69, Issue 3, 27 August 1996, Pages 281-289
Discrete Applied Mathematics

On strongly connected digraphs with bounded cycle length

https://doi.org/10.1016/0166-218X(95)00105-ZGet rights and content
Under a Creative Commons license
open archive

Abstract

Given a directed graph G = (V, E), a natural problem is to choose a minimum number of the edges in E such that, for any two vertices u and v, if there is a path from u to v in E, then there is a path from u to v among the chosen edges. We show that in graphs having no directed cycle with more than three edges, this problem is equivalent to Maximum Bipartite Matching. This leads to a small improvement in the performance guarantee of the previous best approximation algorithm for the general problem.

Cited by (0)

1

Research supported by NSF Research Initiation Award CCR-9307462.

2

Research supported by NSF grant CCR-9409625.

Part of this research was done while at School of ORIE, Cornell University, Ithaca NY 14853 and supported by Éva Tardos' NSF PYI grant DDM-9157199.