Hamiltonian Cycles Passing Through Matchings in k-ary n-cubes

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.