Embedding even cycles on folded hypercubes with conditional faulty edges

Let FFe be the set of vertical bar FFe vertical bar <= 2n - 4 faulty edges in an n-dimensional folded hypercube FQ(n) such that each vertex in FQ(n) is incident to at least two fault-free edges. Under this assumption, we show that every edge of FQ(n) - FFe lies on a fault-free cycle of every even length from 6 to 2(n), where n >= 5. (C) 2015 Elsevier B.V. All rights reserved.