Cyclic one-factorization of the complete graph
type: Item
instance of: scholarly article
title: Cyclic one-factorization of the complete graph
zbMATH Open document ID: 0624.05051
DOI: 10.1016/S0195-6698(85)80020-2
author: Alan Hartman
author: Alexander Rosa
published in: European Journal of Combinatorics
publication date: 1985-01-01T00:00:00Z
review text: Let \(K_ n\) be the complete graph of order n with vertex set V and edge set E. A 1-factorization of \(K_ n\) is a partition of E into n-1 one factors, so that each 1-factor is a partition of V. An automorphism of a 1-factorization is a permutation of V which maps 1-factors onto 1- factors. A 1-factorization is cyclic if it admits an n-cycle as an automorphism. In this paper the authors show that cyclic 1-factorizations exists if and only if n is even and \(n\neq 2^ t\), \(t\geq 3\). They also enumerate cyclic 1-factorizations of \(K_ n\) for \(n\leq 16\).
Mathematics Subject Classification ID: 05C70
zbMATH DE Number: 4012663
zbMATH Keywords: 1-factorization
zbMATH Keywords: automorphism
reviewed by: Louis Caccetta
MaRDI profile type: Publication
cites work: Q4106239
cites work: Q4505277
cites work: Q4075506
cites work: Systems of pairs of cyclic type
full work available at URL: s0195-6698(85)80020-2
OpenAlex ID: W2084761021
description: scientific article; zbMATH DE number 4012663