On Alspach's conjecture with two even cycle lengths
type: Item
instance of: scholarly article
title: On Alspach's conjecture with two even cycle lengths
zbMATH Open document ID: 0978.05059
DOI: 10.1016/S0012-365X(00)00051-0
author: Darryn Bryant
author: P. Adams
author: Abdollah Khodkar
published in: Discrete Mathematics
publication date: 2002-01-27T00:00:00Z
review text: Alspach's conjecture states that if \(\pi\) is a partition of the number \(v(v-1)/2\), for \(v\) odd [of the number \(v(v-2)/2\), for \(v\) even] into \(s\) parts, each at least 3 and at most \(v\), then there exists a decomposition of the complete graph \(K_v\) [of the cocktail-party graph \(K_v-F\)] into \(s\) cycles whose lengths equal the parts of the partition \(\pi\). In this paper, the authors deal with the case when all parts are equal to one of two even numbers \(m\), \(n\), \(m< n\). They show that in this case Alspach's conjecture is true if and only if it is true for all \(v< 7n\). This, together with settling several small cases, makes it possible to show that the Alspach conjecture is true for all even \(m\), \(n\leq 10\).
Mathematics Subject Classification ID: 05C70
Mathematics Subject Classification ID: 05C38
zbMATH DE Number: 1538195
zbMATH Keywords: Alspach's conjecture
zbMATH Keywords: decomposition
zbMATH Keywords: cycles
Wikidata QID: Q123022417
reviewed by: Alexander Rosa
MaRDI profile type: Publication
full work available at URL: s0012-365x(00)00051-0
OpenAlex ID: W2004272279
description: scientific article; zbMATH DE number 1538195