The $2nd-$convex hull of every optimal rectilinear drawing of $K_{n}$ is a triangle
Jesús Leaños, Mario Lomelí, Marcelino Ramírez-Ibáñez, Luis Manuel Rivera-Martínez · arXiv (Cornell University) · 2014
A rectilinear drawing of a graph $G$ is optimal if it has the smallest number of crossings among all rectilinear drawings of $G$. In this paper it is shown that for $n\geq 8$, the second convex hull of every optimal rectilinear drawing of the complete graph $K_n$ is a triangle.