Edge-fault-tolerant edge-bipancyclicity of balanced hypercubes

The balanced hypercube, BHn, is a variant of hypercube Qn. Hao et al. (2014) showed that there exists a fault-free Hamiltonian path between any two adjacent vertices in BHn with (2n−2) faulty edges. Cheng et al. (2015) proved that BHn is 6-edge-bipancyclic after (2n−3) faulty edges occur for all n ≥ 2. In this paper, we improve these two results by demonstrating that BHn is 6-edge-bipancyclic even when there exist (2n−2) faulty edges for all n ≥ 2. Our result is optimal with respect to the maximum number of tolerated edge faults.