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Decomposition of Graphs into Chains

Decomposition of Graphs into Chains We establish a result on edge‐disjoint paths with prescribed ends in infinite trees and apply this to prove the conjecture of Eggleton and Skilton [1] that any connected graph has a decomposition into chains such that at most one of these is one‐way infinite and each vertex is the end‐vertex of at most one of the chains and no vertex of infinite degree is such an end‐vertex. We also give a necessary and sufficient condition for a graph to have a decomposition into one‐way infinite chains. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the London Mathematical Society Wiley

Decomposition of Graphs into Chains

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Publisher
Wiley
Copyright
© London Mathematical Society
ISSN
0024-6093
eISSN
1469-2120
DOI
10.1112/blms/18.3.248
Publisher site
See Article on Publisher Site

Abstract

We establish a result on edge‐disjoint paths with prescribed ends in infinite trees and apply this to prove the conjecture of Eggleton and Skilton [1] that any connected graph has a decomposition into chains such that at most one of these is one‐way infinite and each vertex is the end‐vertex of at most one of the chains and no vertex of infinite degree is such an end‐vertex. We also give a necessary and sufficient condition for a graph to have a decomposition into one‐way infinite chains.

Journal

Bulletin of the London Mathematical SocietyWiley

Published: May 1, 1986

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