### Abstract

Let G = (V,E) be a graph or digraph and r : V → Z_{+}. An r-detachment of G is a graph H obtained by 'splitting' each vertex v ε V into r(v) vertices. The vertices v_{1},..., v_{r(v)} obtained by splitting v are called the pieces of v in H. Every edge uv ε E corresponds to an edge of H connecting some piece of u to some piece of v. Crispin Nash-Williams [9] gave necessary and sufficient conditions for a graph to have a k-edge-connected r-detachment. He also solved the version where the degrees of all the pieces are specified. In this paper, we solve the same problems for directed graphs. We also give a simple and self-contained new proof for the undirected result.

Original language | English |
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Pages (from-to) | 67-77 |

Number of pages | 11 |

Journal | Journal of Graph Theory |

Volume | 43 |

Issue number | 1 |

DOIs | |

Publication status | Published - May 1 2003 |

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### ASJC Scopus subject areas

- Geometry and Topology

### Cite this

*Journal of Graph Theory*,

*43*(1), 67-77. https://doi.org/10.1002/jgt.10104