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AbstractLet F v and F e be sets of faulty vertices and faulty edges, respectively, in the folded hypercube F Q n so that |F v | + |F e | ≤ n − 2, for n ≥ 2. Choose any fault-free edge e. If n ≥ 3 then there is a fault-free cycle of length l in F Q n containing e, for every even l ranging from 4 to 2 n − 2|F v |; if n ≥ 2 is even then there is a fault-free cycle of length l in F Q n containing e, for every odd l ranging from n + 1 to 2 n − 2|F v | − 1.