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The Edge-Disjoint Paths Problem is NP-Complete for Partial k-Trees

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Algorithms and Computation (ISAAC 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1533))

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Abstract

Many combinatorial problems are NP-complete for general graphs, but are not NP-complete for partial k-trees (graphs of treewidth bounded by a constant k) and can be efficiently solved in polynomial time or mostly in linear time for partial k-trees. On the other hand, very few problems are known to be NP-complete for partial k-trees with bounded k. These include the subgraph isomorphism problem and the bandwidth problem. However, all these problems are NP-complete even for ordinary trees or forests. In this paper we show that the edge-disjoint paths problem is NP-complete for partial k-trees with some bounded k, say k = 3, although the problem is trivially solvable for trees.

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Author information

Authors and Affiliations

  1. Graduate School of Information Sciences, Tohoku University, Aoba-yama 05, Sendai, 980-8579, Japan

    Xiao Zhou & Takao Nishizeki

Authors
  1. Xiao Zhou
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  2. Takao Nishizeki
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Korea Advanced Institute of Science and Technology, 373-1, Kusong-dong, Yusong-gu, Taejon, 305-701, Korea

    Kyung-Yong Chwa

  2. Department of Computer Science, University of California, Santa Barbara, CA, 93106, USA

    Oscar H. Ibarra

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© 1998 Springer-Verlag Berlin Heidelberg

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Zhou, X., Nishizeki, T. (1998). The Edge-Disjoint Paths Problem is NP-Complete for Partial k-Trees. In: Chwa, KY., Ibarra, O.H. (eds) Algorithms and Computation. ISAAC 1998. Lecture Notes in Computer Science, vol 1533. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49381-6_44

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  • DOI: https://doi.org/10.1007/3-540-49381-6_44

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-65385-1

  • Online ISBN: 978-3-540-49381-5

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