### Abstract

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|^{3}log|V|). In particular, the integral multicommodity flow problem is proved to belong to the problem class P when the underlying graph is outerplanar.

Original language | English |
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Pages (from-to) | 164-178 |

Number of pages | 15 |

Journal | Journal of Combinatorial Theory, Series B |

Volume | 39 |

Issue number | 2 |

DOIs | |

Publication status | Published - Oct 1985 |

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### ASJC Scopus subject areas

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