On Packable Digraphs

One of the classical results in packing theory states that every graph of order n and size less than or equal to n− 2 is packable in its complement. Moreover, the bound is sharp because the star is not packable. A similar problem arises for digraphs, namely, to find the maximal number fD(n) such that every digraph of order n and size less than or equal to fD(n) is packable. So far it is known that 7 4 n − 81 ≤ fD(n) ≤ 2n − 4 where the upper bound is sharp. In this paper we prove that fD(n) = 2n− o(n).