Hamiltonian paths and cycles, number of arcs and independence number in digraphs

Manoussakis, Y. and D. Amar, Hamiltonian paths and cycles, number of arcs and independence number in digraphs, Discrete Mathematics 105 (1992) 157-172. We let D denote a digraph with n vertices, independence number at least (Y and half-degrees at least k. We give (i) a function f(n, a) (respectively f (n, k, a)) such that any digraph with at least f(n, a) (respectively f(n, k, a)) arcs is Hamiltonian and (ii) a function g(n, a) (respectively g(n, k, a)) such that any digraph with at least g(n, a) (respectively g(n, k, a)) arcs is Hamiltonian connected.