Hamiltonian cycles in hypercubes with more faulty edges

Abstract

ABSTRACTThe hypercube is one of the best known interconnection networks for parallel and distributed systems. In this paper we consider hamiltonian cycles in hypercubes with faulty edges. It is proved that there still exists a fault-free hamiltonian cycle in the hypercube with 3n−7 faulty edges if the following two conditions are satisfied: (1) the degree of every vertex is at least two, (2) there do not exist a forbidden -cycle or -cycle. Our result is optimal in some sense.