On Hamilton Cycle Decompositions of Tensor Products of Graphs

Abstract: A Hamiltonian decomposition of $G$ is a partition of its edge set into disjoint Hamilton cycles. Manikandan and Paulraja conjectured that if $G$ and $H$ are Hamilton cycle decomposable circulant graphs with at least one of them is nonbipartite, then their tensor product is Hamilton cycle decomposable. In this paper, we have proved that, if $G$ is a Hamilton cycle decomposable circulant graph with certain properties and $H$ is a Hamilton cycle decomposable multigraph, then their tensor product is Hamilton cycle decomposable. In particular, tensor products of certain sparse Hamilton cycle decomposable circulant graphs are Hamilton cycle decomposable.