2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/62336The vertex set of the kth cartesian power of a directed cycle of length m can be naturally identified with the set of k-tuples of integers modulo m. For any two vertices v and w of this graph, it is easy to see that if there is a hamiltonian path from v to w, then the sum of the coordinates of v is congruent, modulo m, to one more than the sum of the coordinates of w. We prove the converse, unless k = 2 and m is odd.8 pages, no figuresCombinatorics05C45; 05C25text