Diameter-vulnerability of large bipartite digraphs Original Research Article

In this paper we consider the following problem: Among all bipartite digraphs with n vertices and maximum out-degree d, find one for which the s-diameter-vulnerability (the maximum diameter of the subdigraphs obtained by deleting s vertices) is as small as possible. We give a lower bound and for n = 2(dD − 1 + dD − 3) we find bipartite digraphs with s-diameter-vulnerability at most one larger than this lower bound. These bipartite digraphs have been studied previously by Fiol and Yebra (1990) and found also close to the upper bound on the number of vertices for bipartite digraphs with fixed diameter and maximum degree.