### Abstract

Given a graph G=(V,E) and a set T⊆V, an orientation of G is called T-odd if precisely the vertices of T get odd in-degree. We give a good characterization for the existence of a T-odd orientation for which there exist k edge-disjoint spanning arborescences rooted at a prespecified set of k roots. Our result implies Nash-Williams' theorem on covering the edges of a graph by k forests and a (generalization of a) theorem due to Nebeský on upper embeddable graphs.

Original language | English |
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Pages (from-to) | 37-47 |

Number of pages | 11 |

Journal | Discrete Applied Mathematics |

Volume | 115 |

Issue number | 1-3 |

DOIs | |

Publication status | Published - Nov 15 2001 |

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Applied Mathematics

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## Cite this

Frank, A., Jordán, T., & Szigeti, Z. (2001). An orientation theorem with parity conditions.

*Discrete Applied Mathematics*,*115*(1-3), 37-47. https://doi.org/10.1016/S0166-218X(01)00213-X