Hamilton cycles in tensor product of graphs

AbstractIn this paper, we characterize graphs G for which G⊗K2 is Hamiltonian, where ⊗ denotes the tensor product of graphs. The relationship between the bieulerian orientation of a 4-regular graph G and the existence of a pair of edge-disjoint Hamilton cycles in G⊗K2 is established. Also a characterization for a 4-regular graph to have a bieulerian orientation is presented. Finally, some conjectures of Jha relating to the existence of cycles or edge-disjoint Hamilton cycles are either proved or disproved