Edge-disjoint paths in planar graphs

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Given a planar graph G = (V, E), find k edge-disjoint paths in G connecting k pairs of terminals specified on the outer face of G. Generalizing earlier results of Okamura and Seymour (J. Combin. Theory Ser. B 31 (1981), 75-81) and of the author (Combinatorica 2, No. 4 (1982), 361-371), we solve this problem when each node of G not on the outer face has even degree. The solution involves a good characterization for the solvability and the proof gives rise to an algorithm of complexity O(|V|3log|V|). In particular, the integral multicommodity flow problem is proved to belong to the problem class P when the underlying graph is outerplanar.

Original languageEnglish
Pages (from-to)164-178
Number of pages15
JournalJournal of Combinatorial Theory, Series B
Issue number2
Publication statusPublished - Oct 1985


ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

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