Hamiltonian laceability in hypercubes with faulty edges

It is useful to consider faulty networks because node faults or link faults may occur in networks. In this paper, we investigate hamiltonian properties of conditional faulty hypercubes. Let F be a set of faulty edges in hypercube Qn with n≥4 and |F|≤3n−11. We prove that there still exists a hamiltonian path in Qn−F joining any two vertices of different partite sets if the following two constraints are satisfied: (1) the degree of every vertex in Qn−F is at least 2, and (2) there is at most one vertex with degree 2 in Qn−F.