NP-completeness of some edge-disjoint paths problems Original Research Article

We prove: The directed edge-disjoint paths problem is NP-complete, even if (a) the underlying graph G is acyclic, the demand graph H consists just of three sets of parallel edges and G + H is Eulerian, or (b) G + H is planar, or (c) G is planar and acyclic. (d) The undirected edge-disjoint paths problem is NP-complete, even if G + H is Eulerian and H consists just of three sets of parallel edges.