Notes on a conjecture of Manoussakis concerning Hamilton cycles in digraphs

In 1992, Manoussakis conjectured that a strongly 2-connected digraph D on n vertices is hamiltonian if for every two distinct pairs of independent vertices x, y and w, z we have d(x)+d(y)+d(w)+d(z)≥4n−3. In this note we show that D has a Hamilton path, which gives an affirmative evidence supporting this conjecture.