HAMILTONIAN PATHS AND CYCLES, NUMBER OF ARCS AND INDEPENDENCE NUMBER IN DIGRAPHS

We let D denote a digraph with n vertices, independence number at least-alpha and half-degrees at least k. We give (i) a function f(n, alpha) (respectively f(n, k, alpha)) such that any digraph with at least f(n, alpha) (respectively f(n, k, alpha)) arcs is Hamiltonian and (ii) a function g(n, alpha) (respectively g(n, k, alpha)) such that any digraph with at least g(n, alpha) (respectively g(n, k, alpha)) arcs is Hamiltonian connected.