Edge-fault-tolerant hamiltonicity of augmented cubes

The augmented cube AQ n is a hypercube Q n with additional edges between vertices that differ in a suffix. We show that AQ n with f arbitrary faulty edges contains a copy of Q n with at most n 2 n − 1 f faulty edges. This allows to transfer properties of Q n with faulty edges to AQ n with (more) faulty edges. In particular, we show that if f ⩽ 3 n − 7 and each vertex of AQ n is incident with at least two non-faulty edges then AQ n contains a hamiltonian cycle consisting only of non-faulty edges.