Edge-disjoint Hamiltonian cycles of balanced hypercubes

Abstract

The balanced hypercube, a variant of the hypercube, was proposed as a novel interconnection network of parallel systems. It is known that the balanced hypercube is Hamiltonian. The existence of two edge-disjoint Hamiltonian cycles in balanced hypercubes has remained unknown. In this paper, we prove that the balanced hypercube BHn with n≥2 contains two edge-disjoint Hamiltonian cycles. Further, a linear time algorithm is provided to construct two edge-disjoint Hamiltonian cycles in the balanced hypercube BHn with n≥2.