### Abstract

Let G bean Eulerian digraph, and let {x_{1},x_{2}}, {y_{1}, y_{2}} be two pairs of vertices in G. A directed path from a vertex s to a vertex t is called an st-path. An instance (G; {x_{1}, x_{2}}, {y_{1}, y_{2}}) is called feasible if there is a choice of h,i,j,k with {h,i} = {j,k} = {1,2} such that G has two arc-disjoint X_{h}X_{i}- and y_{j}y_{k}-paths. In this paper, we characterize the structure of minimal infeasible instances, based on which an O(m + n log n) time algorithm is presented to decide whether a given instance is feasible, where n and m are the number of vertices and arcs in the instance, respectively. If the instance is feasible, the corresponding two arc-disjoint paths can be computed in O(m(m + n log n)) time.

Original language | English |
---|---|

Pages (from-to) | 557-589 |

Number of pages | 33 |

Journal | SIAM Journal on Discrete Mathematics |

Volume | 11 |

Issue number | 4 |

DOIs | |

Publication status | Published - Nov 1998 |

### Fingerprint

### Keywords

- Disjoint paths
- Eulerian digraph
- Minimum cut
- Planar graph
- Polynomial time algorithm

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*SIAM Journal on Discrete Mathematics*,

*11*(4), 557-589. https://doi.org/10.1137/S0895480196304970