One-factorizations of regular graphs of order 12
type: Item
instance of: scholarly article
title: One-factorizations of regular graphs of order 12
zbMATH Open document ID: 1062.05120
author: Petteri Kaski
author: Patric R. J. Östergård
published in: The Electronic Journal of Combinatorics
publication date: 2005-04-25T00:00:00Z
full work available at URL: https://eudml.org/doc/124599
full work available at URL: v12i1r2.html
review text: The number of non-isomorphic one-factorizations of \(r\)-regular graphs of order 12 is computed for each possible degree \(r,\) with the exception of \(r=7,8,9\), which remains open after this study. In particular a new approach to one-factorizations of \(K_{12}\) that makes use of triple systems is presented. Some properties of the classified one-factorizations (for instance dealing with the structure of their automorphism group) are also tabulated. The algorithms for graphs with small degree are based on viewing one-factorizations as certain error-correcting codes. Two algorithms are used, one that proceeds a one-factor at a time and one that proceeds a vertex at a time. The discussed algorithms do not utilize a classification of regular graphs.
Mathematics Subject Classification ID: 05C70
Mathematics Subject Classification ID: 05-04
Mathematics Subject Classification ID: 05C85
zbMATH DE Number: 2161303
zbMATH Keywords: triple system
zbMATH Keywords: algorithms
reviewed by: Hans Peter Künzi
describes a project that uses: nauty
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2161303