A note on cycle embedding in hypercubes with faulty vertices

Let f"v denote the number of faulty vertices in an n-dimensional hypercube. This note shows that a fault-free cycle of length of at least 2^n-2f"v can be embedded in an n-dimensional hypercube with f"v=2n-3 and n>=5. This result not only enhances the previously best known result, and also answers a question in [J.-S. Fu, Fault-tolerant cycle embedding in the hypercube, Parallel Computing 29 (2003) 821-832].

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