A Size Condition for Diameter Two Orientable Graphs

It was conjectured by Koh and Tay [Graphs Combin. 18(4) (2002), 745–756] that for $$n\ge 5$$ every simple graph of order n and size at least $$\left( {\begin{array}{c}n\\ 2\end{array}}\right) -n+5$$ has an orientation of diameter two. We prove this conjecture and hence determine for every $$n\ge 5$$ the minimum value of m such that every graph of order n and size m has an orientation of diameter two.