Colouring 4-cycle systems with equitably coloured blocks
type: Item
instance of: scholarly article
title: Colouring 4-cycle systems with equitably coloured blocks
zbMATH Open document ID: 1049.05022
author: Mario Gionfriddo
author: Gaetano Quattrocchi
published in: Discrete Mathematics
publication date: 2004-08-20T00:00:00Z
review text: An \(m\)-colouring of a 4-cycle system of order \(n\) (i.e., of a decomposition of the complete graph \(K_n\) into 4-cycles) is a colouring of the vertices with \(m\) colours; it is equitable if for every 4-cycle two of the four vertices are coloured with one colour, and the other two with another one of the \(m\) colours. The authors investigate the set \(F(n)\) of integers \(m\) such that there exists an equitably \(m\)-coloured 4-cycle system of order \(n\). They show that \(\min F(n)=3\) for every \(n\equiv 1\pmod 8\), \(n\geq 17\) \([F(9)=\varnothing]\), and prove various further results concerning the set \(F(n)\).
Mathematics Subject Classification ID: 05B30
zbMATH DE Number: 2093775
zbMATH Keywords: cycle
zbMATH Keywords: colouring
zbMATH Keywords: chromatic number
zbMATH Keywords: 4-cycle systems
reviewed by: Alexander Rosa
MaRDI profile type: Publication
full work available at URL: j.disc.2003.11.037
OpenAlex ID: W2042908802
cites work: Bicoloring Steiner triple systems
cites work: Q4256358
cites work: Q4026150
cites work: Q4372505
cites work: Upper chromatic number of Steiner triple and quadruple systems
cites work: Strict colouring for classes of Steiner triple systems
cites work: Colouring Steiner systems with specified block colour patterns
cites work: Colouring \(4\)-cycle systems with specified block colour patterns: The case of embedding \(P_3\)-designs
cites work: Decomposition of K//(m,n)(K*//(m,n)) into cycles (circuits) of length 2k
cites work: Q4842710
cites work: Coloring mixed hypergraphs: theory, algorithms and applications
DOI: 10.1016/J.DISC.2003.11.037
description: scientific article; zbMATH DE number 2093775