Finding edge-disjoint paths in partial k-trees

X. Zhou, S. Tamura, T. Nishizeki

Research output: Contribution to journalArticlepeer-review

16 Citations (Scopus)


For a given graph G and p pairs (si, ti), 1 ≤ i ≤ p, of vertices in G, the edge-disjoint paths problem is to find p pairwise edge-disjoint paths Pi, 1 ≤ i ≤ p, 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 the edge-disjoint paths problem is NP-complete even for partial 3-trees. 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.

Original languageEnglish
Pages (from-to)3-30
Number of pages28
Issue number1
Publication statusPublished - 2000


  • Bounded treewidth
  • Edge-coloring
  • Edge-disjoint paths
  • Partial k-tree
  • Polynomial-time algorithm


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