Cycle decompositions of the line graph of \(K_ n\)
type: Item
instance of: scholarly article
title: Cycle decompositions of the line graph of \(K_ n\)
zbMATH Open document ID: 0777.05076
DOI: 10.1016/0097-3165(93)90078-M
author: M. Colby
author: C. A. Rodger
published in: Journal of Combinatorial Theory. Series A
publication date: 1993-05-16T00:00:00Z
review text: A 4-cycle system of a graph \(G\) is a set of 4-cycles that induces a partition of the edge set of \(G\). This note supplements a result of K. Heinrich and G. M. Nonay about a certain set of 4-cycles of \(K_ n\). The proof of the result used a 4-cycle system of the line graph of \(K_ n\). Here the following theorem is proved: If \(n\equiv 1\pmod 8\), then there exists a 4-cycle system of the line graph of \(K_ n\).
Mathematics Subject Classification ID: 05C38
Mathematics Subject Classification ID: 05C70
zbMATH DE Number: 165757
zbMATH Keywords: cycle decomposition
zbMATH Keywords: line graph
reviewed by: Norman F. Quimpo
MaRDI profile type: Publication
cites work: Exact coverings of 2-paths by 4-cycles
cites work: Decomposition of K//(m,n)(K*//(m,n)) into cycles (circuits) of length 2k
full work available at URL: 0097-3165(93)90078-m
OpenAlex ID: W1990180003
description: scientific article; zbMATH DE number 165757