The Formula: see text-ary Formula: see text-cube is a highly efficient interconnect network topology structure, widely recognized for its excellent performance in parallel computing and distributed systems. In this paper, we delve into the study of Hamiltonian cycles passing through prescribed matchings in Formula: see text-ary Formula: see text-cubes. We have obtained the following result: for Formula: see text and odd Formula: see text, every matching with at most Formula: see text edges is contained in a Hamiltonian cycle in the Formula: see text-ary Formula: see text-cube. Our result improves upon some known results, advancing the state of the art in this research area.
Wang et al. (Sat,) studied this question.