A further result on fault-free cycles in faulty folded hypercubes

Folded hypercube is a well-known variation of the hypercube structure and can be constructed from a hypercube by adding a link to every pair of nodes with complementary addresses. Let F F_v (respectively, F F_e) be the set of faulty nodes (respectively, faulty links) in an n-dimensional folded hypercube F Q_n. Fu has showed that F Q_n - F F_v - F F_e for n ≥ 3 contains a fault-free cycle of length at least 2ⁿ - 2 | F F_v | if | F F_v | + | F F_e | ≤ 2 n - 4 and | F F_e | ≤ n - 1. In this paper, we further consider the constraints | F F_v | + | F F_e | ≤ 2 n - 4 and | F F_e | ≥ n that were not covered by Fu's result. We obtain the same lower bound of the longest fault-free cycle length, 2ⁿ - 2 | F F_v |, under the constraints that (1) | F F_v | + | F F_e | ≤ 2 n - 4 and (2) every node in F Q_n is incident to at least two fault-free links.