Hamiltonian decompositions of Cayley graphs on abelian groups of even order
type: Item
instance of: scholarly article
title: Hamiltonian decompositions of Cayley graphs on abelian groups of even order
zbMATH Open document ID: 1021.05047
DOI: 10.1016/S0095-8956(03)00033-9
author: Jiuqiang Liu
published in: Journal of Combinatorial Theory. Series B
publication date: 2003-08-17T00:00:00Z
review text: Let \((A,+)\) be a finite abelian group and \(S\) a subset of \(A\) with \(0\not\in S\). The Cayley graph \(\text{Cay}(A,S)\) is defined to be the graph \(G=(V,E)\) with \(V=A\) and \(E=\{xy\mid x-y\in S\) or \(y-x\in S\}\). Alspach conjectured that any \(2k\)-regular connected Cayley graph on a finite abelian group has a Hamiltonian decomposition, that is, the set of edges admits a partition in \(k\) Hamiltonian circuits [\textit{B. Alspach}, Research problem 59, Discrete Math. 50, 115 (1984)]. J. Liu proved that if \(A\) is an abelian finite group of odd order and \(S\) is a minimal generating set of \(A\), then \(\text{Cay(A,S)}\) has a Hamiltonian decomposition [\textit{J. Liu}, J. Comb. Theory, Ser. B 66, 75-86 (1996; Zbl 0840.05069)]. In this paper the same author shows the following: Let \(A\) be a finite abelian group of even order at least 4 and \(S\) a minimal generating subset of \(A\) such that for any \(s\in S\), the element \(2s\) is not generated by elements in \(S-\{s\}\). Then \(\text{Cay}(A,S)\) has a Hamiltonian decomposition.
reviewed by: Josep M. Brunat
Mathematics Subject Classification ID: 05C25
Mathematics Subject Classification ID: 05C45
Mathematics Subject Classification ID: 05C70
zbMATH DE Number: 1965036
zbMATH Keywords: Hamiltonian decomposition
zbMATH Keywords: Cayley graph
zbMATH Keywords: abelian group
MaRDI profile type: Publication
cites work: Hamiltonian decomposition of Cayley graphs of degree 4
cites work: Pseudo-Cartesian products and Hamiltonian decompositions of Cayley graphs on abelian groups
cites work: Hamiltonian decompositions of products of cycles
cites work: Hamiltonian decompositions of Cayley graphs on Abelian groups
cites work: Hamiltonian decompositions of Cayley graphs on abelian groups of odd order
cites work: Hamiltonian circuits in Cayley graphs
cites work: Hamilton decompositions of Cartesian products of graphs
full work available at URL: s0095-8956(03)00033-9
OpenAlex ID: W1989546358
description: scientific article; zbMATH DE number 1965036