Near 2-factorizations of \(2K_ n:\) Cycles of even length
type: Item
instance of: scholarly article
title: Near 2-factorizations of \(2K_ n:\) Cycles of even length
zbMATH Open document ID: 0729.05039
DOI: 10.1007/BF01788673
published in: Graphs and Combinatorics
publication date: 1989-01-01T00:00:00Z
review text: A near 2-factor in a graph G is a subgraph in which each vertex, except for one vertex of degree zero, has degree 2. A t-uniform near 2- factorization of \(2K_ m\) (two edges between every pair of distinct vertices) is a partition of \(E(2K_ m)\) into near 2-factors all of whose cycles have length t. The authors prove that \(2K_ m\) has a t-uniform near 2-factorization if and only if \(m\equiv l(mod t)\), whenever t is even. They also consider 4-uniform near 2-factorizations of \(2K_ m\) with the property that if one of the near 2-factors is known, all others can easily be generated from it. They find infinitely many m for which there are such 4-uniform near 2-factorizations.
Mathematics Subject Classification ID: 05C70
zbMATH DE Number: 4204386
zbMATH Keywords: near 2-factor
zbMATH Keywords: t-uniform near 2-factorization of \(2K_ m\)
author: James P. Burling
author: Katherine Heinrich
reviewed by: Brian Alspach
MaRDI profile type: Publication
Wikidata QID: Q114233925
cites work: Some observations on the oberwolfach problem
cites work: The Oberwolfach problem and factors of uniform odd length cycles
cites work: Q3698809
cites work: Almost resolvable decomposition of K//n*
cites work: On resolvable balanced incomplete block designs
cites work: Almost resolvable decompositions of \(2K_ n\) into cycles of odd length
cites work: Q3720643
cites work: On a variation of the Oberwolfach problem
cites work: Nesting and almost resolvability of pentagon systems
description: scientific article; zbMATH DE number 4204386