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 f(D)(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 7/4n - 81 <= f(D)(n) <= 2n - 3, where the upper bound is sharp. In this paper we prove that f(D)(n) = 2n - o(n).