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≥ 5 every simple graph of order n and size at least ( [ n; 2 ]) -n+5 has an orientation of diameter two. We prove this conjecture and hence determine for every n≥ 5 the minimum value of m such that every graph of order n and size m has an orientation of diameter two.