# Two arc disjoint paths in Eulerian digraphs

Session 3B

First Online:

## Abstract

Let *G* be an Eulerian digraph, and {*x*_{1}, x_{2}}, {*y*_{1}, y_{2}} be two pairs of vertices in *G*. An instance (*G*; {*x*_{1}, x_{2}}, {*y*_{1}, y_{2}}) is called feasible if it contains two arc-disjoint *x′x″*- and *y′y″*- paths, where {*x*′, *x*″}= {*x*_{1}, x_{2}} and {*y′, y″*}={*y*_{1}, y_{2}}. An *O(m*+*n*log *n*) time algorithm is presented to decide whether *G* is feasible, where *n* and *m* are the number of vertices and arcs in *G*, respectively. The algorithm is based on a structural characterization of minimal infeasible instances.

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© Springer-Verlag Berlin Heidelberg 1995