Hamiltonian paths and cycles, number of arcs and independence number in digraphs (Q1199482)

Let \(D\) denote a digraph with \(n\) vertices, at least \(\alpha\) independent vertices, and in which each vertex has in-degree and out-degree at least \(k\). The authors give bounds, in terms of \(n\) and \(\alpha\), and in terms of \(n\), \(\alpha\), and \(k\), on the number of arcs \(D\) can have without being Hamiltonian or Hamiltonian connected.