### Abstract

Let s, t be vertices of a graph G, and let each edge e have a “capacity” c(e) ∈ R_{+}. We prove a conjecture of Cook and Sebo(combining double acute accent) that for every k ∈ R_{+}, the following two statements are equivalent: (i) there is a “fractional packing” of value k of the odd length s - t paths, so that no edge is used more than its capacity; (ii) for every subgraph H of G with s, t ∈ V(H) in which there is no odd s - t path, [formula] ∑ (c(e): e ∈ E(G) - E(H), and e is incident with v ≥ 2k.

Original language | English (US) |
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Pages (from-to) | 280-288 |

Number of pages | 9 |

Journal | Journal of Combinatorial Theory, Series B |

Volume | 62 |

Issue number | 2 |

DOIs | |

State | Published - Jan 1 1994 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

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

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## Cite this

Schrijver, A., & Seymour, P. D. (1994). Packing odd paths.

*Journal of Combinatorial Theory, Series B*,*62*(2), 280-288. https://doi.org/10.1006/jctb.1994.1070