Abstract

This paper considers the problem of many-to-many disjoint paths in the hypercube Qn with fv faulty vertices and fe faulty edges, and obtains the following result. For any integer k with 1⩽k⩽n-1, any two sets S and T of k fault-free vertices in different parts, if fv+fe⩽n-k-1, then there exist k disjoint fault-free (S,T)-paths in Qn which contains at least 2n-2fv vertices. This result is optimal in the worst case.

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