Ring embedding in faulty augmented cubes

Abstract

In this paper, we consider the fault hamiltonicity and the fault Hamiltonian connectivity of the augmented cubes AQ/sub n/. Assume that F /spl sube/ V(AQ/sub n/) /spl cup/ E(AQ/sub n/) and n /spl ges/ 4. We prove that AQ/sub n/ - F is Hamiltonian if |F| /spl les/ 2n-3 and that AQ/sub n/ - F is Hamiltonian connected if |F| /spl les/ 2n - 4. Moreover, these bounds are tight.