A Chvátal-Erdős condition for Hamilton cycles in digraphs (Q1095153)

The main result is the following sufficient condition for a digraph D to be Hamiltonian formulated in terms of its connectivity and independence number \(\alpha_ 2(D)\) (i.e. the largest number of vertices in D such that no two of them are contained in a common 2-cycle of D): Let D be a digraph whose independence number \(\alpha_ 2(D)\leq a\). If the connectivity number of D is \(\geq 2^ a(a+2)!\) then D is Hamiltonian.