The varietal hypercube VQn,a variant of the hypercube Qn,was studied.It was proved that VQn contains a fault-free Hamilton cycle provided faulty edges do not exceed n-2,and that for two distinct vertices,x and y,there is a fault-free xy-Hamilton path in VQn provided faulty edges do not exceed n-3 for n≥3.The proof is based on an inductive construction.
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