On the number of visibility graphs of simple polygons (Q5937456)

A visibility graph of order \(n\) is what can be seen as the graph obtained from an \(n\)-gon on the plane by adding all the edges each represented by the straight segment between the two ends (vertices of the \(n\)-gon) in the inner domain of the \(n\)-gon. It is asked how many distinct labeled graphs of order \(n\) are visibility graphs. However, it is generally not easy to get an exact answer. This paper provides that the number of visibility graphs of order \(n\) is roughly in the range between \(O(n^2)\) and \(O(n^3)\).