Six-cycle systems
type: Item
instance of: scholarly article
title: Six-cycle systems
zbMATH Open document ID: 1482.05275
author: Mariusz Meszka
author: Alexander Rosa
published in: Mathematica Slovaca
publication date: 2021-12-03T00:00:00Z
review text: In this paper, the authors survey the existing results on \(6\)-cycle systems. The topics covered are the following: existence of \(6\)-cycle systems with additional properties, enumeration results, embeddings, resolvable and almost resolvable \(6\)-cycle systems, colourings, \(2\)-perfect and almost \(2\)-perfect \(6\)-cycle systems, \(6\)-cycle systems with higher index, metamorphoses, nested \(6\)-cycles systems, intersections, decompositions of bipartite and multipartite graphs in \(6\)-cycle systems, packings and coverings, directed \(6\)-cycles. Moreover, a few enumeration results are included here for the first time. At the end of the paper, the authors give a list of open problems related to \(6\)-cycle systems.
reviewed by: Paola Bonacini
Mathematics Subject Classification ID: 05C70
Mathematics Subject Classification ID: 05C51
Mathematics Subject Classification ID: 05B07
Mathematics Subject Classification ID: 05C30
zbMATH DE Number: 7438361
zbMATH Keywords: graph decompositions
zbMATH Keywords: six-cycle systems
MaRDI profile type: Publication
full work available at URL: ms-2021-0003
OpenAlex ID: W3173236514
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Six-cycle systems (DOI)
DOI: 10.1515/MS-2021-0003