Directed Hamilton Cycle Decompositions of the Tensor Product of Symmetric Digraphs

Abstract

The first two authors have shown, in $[13]$, that if $K_{r,r}\times K_m$, $m\ge 3$, is an even regular graph, then it is Hamilton cycle decomposable, where $\times$ denotes the tensor product of graphs. In this paper, it is shown that if $(K_{r,r}\times K_m{)}^{\ast }$ is odd regular, then $(K_{r,r}\times K_m{)}^{\ast }$ is directed Hamilton cycle decomposable, where $(K_{r,r}\times K_m{)}^{\ast }$ denotes the symmetric digraph of $K_{r,r}\times K_m$.