Fault-free Hamiltonian cycles in crossed cubes with conditional link faults

The crossed cube, which is a variation of the hypercube, possesses some properties superior to the hypercube. In this paper, assuming that each node is incident with at least two fault-free links, we show that an n-dimensional crossed cube contains a fault-free Hamiltonian cycle, even if there are up to 2n − 5 link faults. The result is optimal with respect to the number of link faults tolerated. We also verify that the assumption is practically meaningful by evaluating its occurrence probability, which is very close to 1.