Existence of cyclic \(k\)-cycle systems of the complete graph
type: Item
instance of: scholarly article
title: Existence of cyclic \(k\)-cycle systems of the complete graph
zbMATH Open document ID: 1013.05023
DOI: 10.1016/S0012-365X(02)00463-6
author: Marco Buratti
author: Alberto Del Fra
published in: Discrete Mathematics
publication date: 2003-03-16T00:00:00Z
review text: The existence problems for cyclic \(k\)-cycle systems of the complete graph \(K_v\) with \(k \equiv 1\) (mod \(2k\)) and of the complete \(m\)-partite graph \(K_{m \times k}\) with odd \(m\) and \(k\) are considered. The authors give explicit constructions for all admissible cases using Rosa and Skolem sequences for suitable parameters. In particular, they prove that a cyclic \(p\)-cycle system of \(K_v\) with prime \(p\) exists for all admissible values of \(p\) and \(v\) but \((p,v)=(3,9)\).
Mathematics Subject Classification ID: 05B30
Mathematics Subject Classification ID: 05C38
zbMATH DE Number: 1882213
zbMATH Keywords: Rosa sequence
zbMATH Keywords: Skolem sequence
reviewed by: Peter Boyvalenkov
MaRDI profile type: Publication
full work available at URL: s0012-365x(02)00463-6
OpenAlex ID: W2007349912
description: scientific article; zbMATH DE number 1882213