Finding edge-disjoint paths in partial k-trees

An extended abstract
  • Xiao Zhou
  • Syurei Tamura
  • Takao Nishizeki
Session 6a: Invited Presentation
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1178)


For a given graph G and p pairs (si, ti), 1≤ip, of vertices in G, the edge-disjoint paths problem is to find p pairwise edge-disjoint paths Pi, 1≤ip, connecting si and ti. Many combinatorial problems can be efficiently solved for partial k-trees (graphs of treewidth bounded by a fixed integer k), but it has not been known whether the edge-disjoint paths problem can be solved in polynomial time for partial k-trees unless p=O(1). This paper gives two algorithms for the edge-disjoint paths problem on partial k-trees. The first one solves the problem for any partial k-tree G and runs in polynomial time if p=O(log n) and in linear time if p=O(1), where n is the number of vertices in G. The second one solves the problem under some restriction on the location of terminal pairs even if p ≥ log n.

Key words

edge-disjoint paths partial k-tree bounded tree-width polynomial-time algorithm edge-coloring 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Xiao Zhou
    • 1
  • Syurei Tamura
    • 1
  • Takao Nishizeki
    • 1
  1. 1.Graduate School of Information SciencesTohoku UniversitySendaiJapan

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