A conjecture concerning strongly connected graphs (Q1301281)

Let \(G\) be a strongly connected digraph without loops and multiple arcs such that \(G\) has \(n\) vertices and \(d\) arcs. It is shown in the paper that if \(n\leq 5\) and \(d\geq n(n-1)/2+1\) then there is a vertex \(v\) in \(G\) so that \(G-v\) is strongly connected as well. It is conjectured that the statement is true for any \(n\).