Fault-tolerant embedding of paths in crossed cubes

The crossed cube CQn is an important variant of the hypercube Qn and possesses many desirable properties for interconnection networks. This paper shows that in CQn with fv faulty vertices and fe faulty edges there exists a fault-free path of length ℓ between any two distinct fault-free vertices for each ℓ satisfying 2n−1−1≤ℓ≤2n−fv−1 provided that fv+fe≤n−3, where the lower bound of ℓ and the upper bound of fv+fe are tight for some n. Moreover, this result improves the known result that CQn is (n−3)-Hamiltonian connected.