Conditional edge-fault-tolerant edge-bipancyclicity of hypercubes

The hypercube has been one of the most popular interconnection networks for parallel computer/communication systems. In this paper, we assume that each node is incident with at least two fault-free links. Under this assumption, we show that every fault-free edge lies on a fault-free cycle of every even length from 6 to 2n inclusive, even if it has up to 2n − 5 link faults. The result is optimal with respect to the number of link faults tolerated.