TY - JOUR

T1 - The edge-disjoint paths problem is NP-complete for series-parallel graphs

AU - Nishizeki, Takao

AU - Vygen, Jens

AU - Zhou, Xiao

N1 - Copyright:
Copyright 2005 Elsevier B.V., All rights reserved.

PY - 2001/11/15

Y1 - 2001/11/15

N2 - 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.

AB - 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.

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U2 - 10.1016/S0166-218X(01)00223-2

DO - 10.1016/S0166-218X(01)00223-2

M3 - Article

AN - SCOPUS:0035980930

VL - 115

SP - 177

EP - 186

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

SN - 0166-218X

IS - 1-3

ER -