Edge-fault-tolerant hamiltonicity of augmented cubes

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