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

Abstract

As a variant of the well-known hypercube, the balanced hypercube $$BH_n$$ was proposed as a desired interconnection network topology for parallel computing. It is known that $$BH_n$$ is bipartite. Assume that $$S=\{s_1,s_2\}$$ and $$T=\{t_1,t_2\}$$ are any two sets of vertices in different partite sets of $$BH_n$$ ( $$n\ge 1$$ ). It has been proved that there exist two vertex-disjoint $$s_1,t_1$$ -path and $$s_2,t_2$$ -path of $$BH_n$$ covering all vertices of $$BH_n$$ . In this paper, we prove that there always exist two vertex-disjoint $$s_1,t_1$$ -path and $$s_2,t_2$$ -path covering all vertices of $$BH_n$$ ( $$n\ge 2$$ ) with at most $$2n-3$$ faulty edges. The upper bound $$2n-3$$ of edge faults can be tolerated is optimal.