Hamiltonian cycles through prescribed edges in k-ary n-cubes.

We prove that if P is a set of at most 2n − 1 edges in a k-ary n-cube, where k ≥ 4 and n ≥ 2, then there is a Hamiltonian cycle on which every edge of P lies if, and only if, the subgraph of the k-ary n-cube induced by the edges of P is a vertex-disjoint collection of paths. This answers a question posed by Wang, Li and Wang who proved the analogous result for 3-ary n-cubes