Fault-tolerant cycle embedding in the hypercube with more both faulty vertices and faulty edges

Let fv (respectively, fe) denote the number of faulty vertices (respectively, edges) in an n-dimensional hypercube. In this paper, we show that a fault-free cycle of length of at least 2n − 2fv can be embedded in an n-dimensional hypercube with fe ⩽ n − 2 and fv + fe ⩽ 2n − 4. Our result not only improves the previously best known result of [A. Sen, A. Sengupta, S. Bandyopadhyay, On some topological properties of hypercube, incomplete hypercube and supercube, in: Proceedings of the International Parallel Processing Symposium, Newport Beach, April, 1993, pp. 636–642] where fv > 0 or fe ⩽ n − 2 and fv + fe ⩽ n − 1 were assumed, but also extends the result of [J.-S. Fu, Fault-tolerant cycle embedding in the hypercube, Parallel Computing 29 (2003) 821–832] where only the faulty vertices are considered.