On the Hamiltonicity of the Cartesian Product Vassilios V. Dimakopoulos ∗ Leonidas Palios ∗ Athanasios S. Poulakidas † Abstract We examine the hamiltonicity of the cartesian product P = G 1 × G 2 of two graphs G 1 , G 2 . We provide necessary and/or sufficient conditions for P to be hamiltonian, depending on the hamiltonian properties of G 1 and G 2 , with corresponding constructions. We also prove a conjecture by Batagelj and Pisanski related to the ‘cyclic hamiltonicity’ of a graph. Keywords: cartesian product, graphs, hamiltonian cycles, interconnection networks 1 Introduction An undirected graph G =(V,E) is said to be hamiltonian if it contains a spanning cycle. If it contains a spanning path then G is called traceable. The problem of determining whether a graph is hamiltonian or traceable has been fundamental in graph theory. This and related problems have been extensively surveyed (see for example [3, 6]). * Department of Computer Science, University of Ioannina, P.O. Box 1186, 45110 Ioannina, Greece. E-mail: dimako@cs.uoi.gr, palios@cs.uoi.gr. † Department of Computer Engineering and Informatics, University of Patras, 26500 Patras, Greece. E-mail: poulak@ceid.upatras.gr 1