Highly edge-connected detachments of graphs and digraphs

  • Authors:

  • Alex R. Berg;Bill Jackson;Tibor Jordán

  • Affiliations:

  • Brics, Department of Computer Science, University of Aarhus, NY Munkegade Building 540, 8000 Aarhus C, Denmark;School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, London E1 4NS, England;Department of Operations Research, Eötvös University, Pázmány Péter Sétány 1-C, 1117 Budapest, Hungary

  • Venue:
  • Journal of Graph Theory
  • Year:
  • 2003

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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 ν ∈ V into r(ν) vertices. The vertices ν1,…,νr(ν) obtained by splitting ν are called the pieces of ν in H. Every edge uν ∈ E corresponds to an edge of H connecting some piece of u to some piece of ν. 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. © 2003 Wiley Periodicals, Inc. J Graph Theory 43: 67–77, 2003 This work is dedicated to the memory of Crispin Nash-Williams.