... 1 for < /b> i = |A+| +1, ,m and j = ρn +1, ,2ρn.DenotethisblockM2.DenotebyM3 the < /b> block consisting of < /b> the < /b> rows i = |A+|+1, ,m and the < /b> columnsj =1, ,ρn.DenotebyM4 the < /b> block consisting of < /b> the < /b> ... to [1]. In < /b> this paper we consider the< /b> most basic Tur´an-type problem in < /b> bipartite digraphs, namely, specifying conditions on < /b> the< /b> cardinality of < /b> the < /b> edge-set of < /b> the < /b> digraph that guarantee the < /b> existence ... and B in < /b> G(R, S)tothemaximum number of < /b> cycles in < /b> a cycle decomposition of < /b> an Eulerian bipartite digraphthat corresponds to A − B, together with the < /b> upper bound for < /b> b( m, n), it is shown in< /b> [3]...