Oriented paths in mixed graphs

Authors:
Egon Wanke;Rolf Kötter
Affiliations:
Institute of Computer Science;C & O.Vogt Brain Research Institute, and Institute of Anatomy II, Heinrich-Heine-Universität, Düsseldorf, Germany
Venue:
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
Year:
2004

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Abstract

We consider mixed graphs with directed and undirected edges A path in a mixed graph is called oriented if it has at least one directed edge We show that 1.) oriented paths can be found in polynomial time, 2.) computing a maximal number of mutually edge-disjoint oriented s,t-paths is NP-complete, and 3.) computing a minimal set of edges or vertices whose removal destroys all oriented s,t-paths is NP-complete In mixed graphs, the gap between the maximal number of mutually edge-disjoint oriented s,t-paths and the minimal number of edges or vertices in an s,t-cut can be arbitrary large Finally we introduce simple 2-approximation algorithms for computing vertex and edge s,t-cuts.