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

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