Unpaired many-to-many disjoint path cover of balanced hypercubes
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The balanced hypercube BH_n, which is a variant of the hypercube, was proposed as a desired interconnection network topology. It is known that BH_n is bipartite. Assume that S={s_1,s_2,...,s_2n-2} and T={t_1,t_2,...,t_2n-2} are any two sets of vertices in different partite sets of BH_n (n≥2). It has been proved that there exists paired 2-disjoint path cover of BH_n. In this paper, we prove that there exists (2n-2)-disjoint path cover of BH_n (n≥2) from S to T, which partially improved some known results. The upper bound 2n-2 of the number of disjoint paths in unpaired (2n-2)-disjoint path cover is optimal.
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