Hamiltonian laceability of hypercubes with some faulty elements

An n-dimensional hypercube Q_n is well known as bipartite and one of the most efficient networks for parallel computation. Fault tolerance is an important issue for a network since the vertex (or edge) in the network may fail sometimes. Assume that n ges 4 and P is a faulty path (or cycle) of order les 2n - 4 in Q_n. We prove that Q_n - P is Hamiltonian laceable. Furthermore, the bound is tight.