Embedding digraphs of small size Original Research Article

Let D=(V,A) be a digraph without loops and multiple arcs of order n ⩾ 2. We say that D is embeddable if there is a permutation φ : V → V (called complementing permutation) such that (φ(x), φ(y)) ∉ A for every arc (x, y) ϵ A. In this paper we prove that if | A | < [3(n - 2)/2] then D is embeddable and, moreover, there is a complementing permutation which is a composition of disjoint transpositions when n is even or a composition of disjoint transpositions and a fixed point when n is odd.