LARGE (D,D,D',S)-BIPARTITE DIGRAPHS

A (d, D, D', s)-digraph is a directed graph with diameter D and maximu m out-degree d such that after the deletion of any s of its vertices t he resulting digraph has diameter at most D'. Our concern is to find l arge, i.e. with order as large as possible, (d, D, D', s)-bipartite di graphs. To this end, it is proved that some members of a known family of large bipartite digraphs satisfy a Menger-type condition. Namely, b etween any pair of non-adjacent vertices they have s + 1 internally di sjoint paths of length at most D'. Then, a new family of (d,D,D',s)-bi partite digraphs with order very close to the upper bound is obtained.