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.
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics