Extremal graphs of order dimension 4 - Agnarsson, Geir (Mathematica Scandinavica, 2002)
We study the maximal number of edges of a graph on p vertices of order dimension 4. We will show that the lower bound for this number is greater than 38p^2 + 2p - 13. In particular the Turn-4 graph on p vertices does not have the maximal number of edges among the graphs of order dimension 4.