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Highly edge-connected detachments of graphs and digraphs

✍ Scribed by Alex R. Berg; Bill Jackson; Tibor Jordán

Publisher: John Wiley and Sons
Year: 2003
Tongue: English
Weight: 107 KB
Volume: 43
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.10104

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✦ Synopsis

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 ν~1~,…,ν~r(ν)~ obtained by splitting ν are called the pieces of ν in H. Every edge __u__ν ∈ 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

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