Fault-free Hamiltonian cycles in faulty butterfly graphs

Butterfly graphs were originally defined as the underlying graphs of fast Fourier transform (FFT) networks, which can perform the FFT very efficiently. Since butterfly graphs are regular, of degree four, they can tolerate at most two edge faults in the worst case in order to establish a Hamiltonian cycle. In this paper, we show that a butterfly graph contains a fault-free Hamiltonian cycle even if it has two random edge faults.