On the rectilinear crossing number of complete graphs

We prove a lower bound of 0.3288   n 4¡ for the rectilinear crossing number cr(Kn) of a complete graph on n vertices, or in other words, for the minimum number of convex quadrilaterals in any set of n points in general position in the Euclidean plane. As we see it, the main contribution of this paper is not so much the concrete numerical improvement over earlier bounds, as the novel method of proof, which is not based on bounding cr(Kn) for some small n.

• Type: Conference
• Year: 2003
• Where: SODA
• Authors: Uli Wagner
• Keywords: Algorithms, Concrete Numerical Improvement, Convex Quadrilaterals, Rectilinear Crossing Number, SODA 2003