Embedding Two Edge-Disjoint Hamiltonian Cycles into Parity Cubes

Abstract

Edge-disjoint Hamiltonian cycles are helpful to implement efficient and fault tolerant algorithms that require a ring structure. The n-dimensional parity cube, PQn, is a variant of hypercube. The existence of two edge-disjoint Hamiltonian cycles in parity cube is unknown. In this paper, we prove that there exist two edge-disjoint Hamiltonian cycles in n-dimensional parity cube with n≥4.