On geometric graphs with no two edges in convex position (Q1387850)

A geometric graph is a graph \(G= (V,E)\) drawn in the plane, whose vertex set is represented by points in general position and whose edges are represented by straight segments. Two edges of a geometric graph are in convex position if they are disjoint edges of a convex quadrilateral. The main result states that a geometric graph with \(n\) vertices and no pair of edges in convex position contains at most \(2n-1\) edges.