On hamiltonian decompositions of tensor products of graphs

Finding a hamiltonian decomposition of G is one of the challenging problems in graph theory. We do not know for what classes of graphs G and H, their tensor product G x H is hamiltonian decomposable. In this paper, we have proved that, if G is a hamiltonian decomposable circulant graph with certain properties and H is a hamiltonian decomposable multigraph, then G x H is hamiltonian decomposable. In particular, tensor products of certain sparse hamiltonian decomposable circulant graphs are hamiltonian decomposable.

Hamiltonian decompositions of prisms over complete 3-uniform hypergraphs

We consider prisms over complete 3-uniform hypergraphs and decompose them into Hamiltonian cycles of Katona–Kierstead type. We show that prisms over complete 3-uniform hypergraphs of order 4, 5 and 8 can be decomposed into Hamiltonian cycles and we suggest that prisms over complete 3-uniform hypergraphs of order in the form 6t + 2 may have Hamiltonian decompositions.