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 -