Nesting of cycle systems of odd length
type: Item
instance of: scholarly article
title: Nesting of cycle systems of odd length
zbMATH Open document ID: 0714.05014
DOI: 10.1016/0012-365X(89)90360-9
author: C. A. Rodger
author: D. R. Stinson
author: C. C. Lindner
published in: Discrete Mathematics
publication date: 1989-01-01T00:00:00Z
review text: A nesting of an m-cycle system \((K_ n,L)\) is equivalent to an edge decomposition of \(2K_ n\) into wheels, each with m spokes with the property that for each pair of vertices x and y, one of the edges \(\{\) x,y\(\}\) occurs on the rim of a wheel and one of the edges \(\{\) x,y\(\}\) is a spoke of a wheel. In this paper the authors prove that for any odd m, the spectrum of m-cycle systems which can be nested is the set of all \(m\equiv 1\) (mod 2m) with at most 13 possible exceptions for each m. Some of these exceptions are then removed for some small values of m. For a recent survey of nested cycle systems, see the third author [The construction of nested cycle systems, Coding Theory and Design Theory, Part I: Coding theory, Proc. Workshop IMA Program Appl. Comb., Minneapolis/MN (USA) 1987-88, IMA Vol. Math. Appl. 20, 362-367 (1990)].
Mathematics Subject Classification ID: 05B30
Mathematics Subject Classification ID: 05C70
Mathematics Subject Classification ID: 05B07
zbMATH DE Number: 4174943
zbMATH Keywords: nesting
zbMATH Keywords: m-cycle system
zbMATH Keywords: edge decomposition
zbMATH Keywords: wheels
zbMATH Keywords: spectrum
zbMATH Keywords: nested cycle systems
MaRDI profile type: Publication
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Wikidata QID: Q127847464
description: scientific article; zbMATH DE number 4174943