Abstract: The Tree-hypercubes network TH(s, d) is an interconnection network that is recursively defined and has excellent properties for scalable message passing computer systems. In this study we describe the ability of a TH(s, d) to implement algorithms that use the communication pattern of linear array and a ring to formulate a Hamiltonian cycle. We propose an algorithm for mapping a ring onto a tree-hypercubes which results in a dilation and congestion of one.