On the hamiltonicity of the cartesian product

We examine the hamiltonicity of the cartesian product P=G1×G2 of two graphs G1, G2. We provide necessary and/or sufficient conditions for P to be hamiltonian, depending on the hamiltonian properties of G1 and G2, with corresponding constructions. We also prove a conjecture by Batagelj and Pisanski related to the 'cyclic hamiltonicity' of a graph.