Directed Hamilton Cycle Decompositions of the Tensor Product of Symmetric Digraphs

Abstract

The first two authors have shown, in \([13]\), that if \(K_{r,r} \times K_{m}\), \(m \geq 3\), 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 \((K_{r,r} \times K_{m})^*\) is odd regular, then \((K_{r,r} \times K_{m})^*\) is directed Hamilton cycle decomposable, where \((K_{r,r} \times K_{m})^*\) denotes the symmetric digraph of \(K_{r,r} \times K_{m}\).