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 v1,..., vr(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  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.
ASJC Scopus subject areas
- Geometry and Topology