Fault hamiltonicity of augmented cubes

In this paper, we consider the fault hamiltonicity and the fault hamiltonian connectivity of the augmented cubes AQn. Assume that F ⊆ V(AQn) ∪ E(AQn) and n ⩾ 4. We prove that AQn − F is hamiltonian if ∣F∣ ⩽ 2n − 3 and that AQn − F is hamiltonian connected if ∣F∣ ⩽ 2n − 4. Moreover, these bounds are tight.