The unpaired many-to-many k-disjoint paths in bipartite hypercube-like networks

Abstract

In this paper, we discuss about the problem of unpaired many-to-many disjoint paths in bipartite hypercube-like networks with faulty elements. Let F be a faulty set with f faulty elements in an n-dimensional bipartite hypercube-like network G. For every positive integer k≥1 satisfying f+k≤n−1, and two arbitrary sets S and T with k fault-free vertices in distinct parts of the bipartition of G, there exists an unpaired fault-free k-disjoint path collection joining S and T in G−F, which contains at least 2n−2fv vertices, where fv is the number of faulty vertices in G. This result is optimal in the worst case, and the bound f+k≤n−1 is tight.