Highly edge-connected detachments of graphs and digraphs

Alex R. Berg, Bill Jackson, Tibor Jordán

Research output: Contribution to journalArticle

9 Citations (Scopus)


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 [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 languageEnglish
Pages (from-to)67-77
Number of pages11
JournalJournal of Graph Theory
Issue number1
Publication statusPublished - May 1 2003


ASJC Scopus subject areas

  • Geometry and Topology

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