Many-to-many disjoint paths in hypercubes with faulty vertices

This paper considers the problem of many-to-many disjoint paths in the hypercube Q n with f faulty vertices and obtains the following result. For any integer k with 1 ź k ź n - 1 and any two sets S and T of k fault-free vertices in different partite sets of Q n ( n ź 2 ) , if f ź 2 n - 2 k - 2 and each fault-free vertex has at least two fault-free neighbors, then there exist k fully disjoint fault-free paths linking S and T which contain at least 2 n - 2 f vertices. A linear algorithm for finding such disjoint paths is also given. This result improves some known results in a sense.

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