Paired many-to-many two-disjoint path cover of balanced hypercubes with faulty edges

As a variant of the well-known hypercube, the balanced hypercube BHn was proposed as a desired interconnection network topology for parallel computing. It is known that BHn is bipartite. Assume that S={s1,s2} and T={t1,t2} are any two sets of vertices in different partite sets of BHn (n1). It has been proved that there exist two vertex-disjoint s1,t1-path and s2,t2-path of BHn covering all vertices of BHn. In this paper, we prove that there always exist two vertex-disjoint s1,t1-path and s2,t2-path covering all vertices of BHn (n2) with at most 2n-3 faulty edges. The upper bound 2n-3 of edge faults can be tolerated is optimal.