Non-separable detachments of graphs

Bill Jackson, T. Jordán

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

Let G = (V, E) be a graph 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, 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. An r-degree specification for G is a function f on V, such that, for each vertex v ε V, f (v) is a partition of d(v) into r(v) positive integers. An f-detachment of G is an r-detachment H in which the degrees in H of the pieces of each v ε V are given by f (v). Crispin Nash-Williams [3] obtained necessary and sufficient conditions for a graph to have a k-edge-connected r-detachment or f-detachment. We solve a problem posed by Nash-Williams in [2] by obtaining analogous results for non-separable detachments of graphs.

Original languageEnglish
Pages (from-to)17-37
Number of pages21
JournalJournal of Combinatorial Theory. Series B
Volume87
Issue number1
DOIs
Publication statusPublished - Jan 2003

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Nonseparable
Specifications
Graph in graph theory
Vertex of a graph
Partition
Specification
Necessary Conditions
Integer
Sufficient Conditions

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

Non-separable detachments of graphs. / Jackson, Bill; Jordán, T.

In: Journal of Combinatorial Theory. Series B, Vol. 87, No. 1, 01.2003, p. 17-37.

Research output: Contribution to journalArticle

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