Embedding paths into the 4-ary n-cube with faulty nodes

A k-ary n-cubes Q^k_n is an important network for information transportation. In this paper, we research 4-ary n-cubes, and prove that a 4-ary n-cube with f ≤ n-1 faulty vertices admits a fault-free path of every even length from 2n to 4ⁿ -2f -2 between any two healthy vertices υ = υ_n-1 υ_n-2 ... υ₀, υ = υ_n-1 υ_n-2 ... υ₀ with υ_j = u_j ± 2 (mod 4), j ϵ {0, 1, ... n-1} and υ_i i ϵ {0, 1, ..., n-1}{_j}.