Many combinatorial problems are NP-complete for general graphs. However, when restricted to series-parallel graphs or partial k-trees, many of these problems can be solved in polynomial time, mostly in linear time. On the other hand, very few problems are known to be NP-complete for series-parallel graphs or partial k-trees. These include the subgraph isomorphism problem and the bandwidth problem. However, these problems are NP-complete even for trees. In this paper, we show that the edge-disjoint paths problem is NP-complete for series-parallel graphs and for partial 2-trees although the problem is trivial for trees and can be solved for outerplanar graphs in polynomial time. © 2001 Elsevier Science B.V.
Nishizeki, T., Vygen, J., & Zhou, X. (2001). The edge-disjoint paths problem is NP-complete for series-parallel graphs. Discrete Applied Mathematics, 115(1–3), 177–186. https://doi.org/10.1016/S0166-218X(01)00223-2