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