Hamiltonian decomposition of complete tripartite 3-uniform hypergraphs
type: Item
instance of: scholarly article
zbMATH Open document ID: 1341.05177
author: Ratinan Boonklurb
author: Sirirat Singhun
author: Sansanee Termtanasombat
publication date: 2016-02-23T00:00:00Z
Mathematics Subject Classification ID: 05C65
Mathematics Subject Classification ID: 05C45
zbMATH DE Number: 6544901
zbMATH Keywords: \(k\)-uniform hypergraph
zbMATH Keywords: Hamiltonian decomposition
zbMATH Keywords: 1-factor
zbMATH Keywords: orthogonal quasigroup
MaRDI profile type: Publication
title: Hamiltonian decomposition of complete tripartite 3-uniform hypergraphs
published in: East-West Journal of Mathematics
review text: A complete tripartite 3-uniform hypergraph \(K_{m,m,m}^{(3)} \) has its vertex set \(V\) partitioned into three subsets \(V_1\), \(V_2\) and \(V_3\) of cardinality \(m\) and its edges are all 3-subsets of vertices which are not contained in any of the \(V_i\). A Hamiltonian cycle in a 3-uniform hypergraph is a cyclic ordering of its vertices such that every consecutive 3-tuple of vertices is an edge. The purpose of the paper under review is to show that the necessary condition for \(K_{m,m,m}^{(3)} \) to have a Hamiltonian decomposition, namely that \(m\) is divisible by 3, is also sufficient. The proof is constructive and uses 1-factors and orthogonal quasigroups.
reviewed by: Brigitte Servatius
description: scientific article; zbMATH DE number 6544901