### Abstract

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.

Original language | English |
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Pages (from-to) | 177-186 |

Number of pages | 10 |

Journal | Discrete Applied Mathematics |

Volume | 115 |

Issue number | 1-3 |

DOIs | |

Publication status | Published - 2001 Nov 15 |

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Applied Mathematics

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## Cite this

*Discrete Applied Mathematics*,

*115*(1-3), 177-186. https://doi.org/10.1016/S0166-218X(01)00223-2