### 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 |
---|---|

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 - 1985 |

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### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

**Edge-disjoint paths in planar graphs.** / Frank, A.

Research output: Contribution to journal › Article

*Journal of Combinatorial Theory. Series B*, vol. 39, no. 2, pp. 164-178. https://doi.org/10.1016/0095-8956(85)90046-2

}

TY - JOUR

T1 - Edge-disjoint paths in planar graphs

AU - Frank, A.

PY - 1985

Y1 - 1985

N2 - 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.

AB - 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.

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UR - http://www.scopus.com/inward/citedby.url?scp=0001002826&partnerID=8YFLogxK

U2 - 10.1016/0095-8956(85)90046-2

DO - 10.1016/0095-8956(85)90046-2

M3 - Article

VL - 39

SP - 164

EP - 178

JO - Journal of Combinatorial Theory. Series B

JF - Journal of Combinatorial Theory. Series B

SN - 0095-8956

IS - 2

ER -