A note on fault-free mutually independent Hamiltonian cycles in hypercubes with faulty edges

Abstract

In the paper "Fault-free Mutually Independent Hamiltonian Cycles in Hypercubes with Faulty Edges" (J. Comb. Optim. 13:153-162, 2007), the authors claimed that an n-dimensional hypercube can be embedded with (n-1-f)-mutually independent Hamiltonian cycles when fa parts per thousand currency signn-2 faulty edges may occur accidentally. However, there are two mistakes in their proof. In this paper, we give examples to explain why the proof is deficient. Then we present a correct proof.