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SODA
2003
ACM

On the rectilinear crossing number of complete graphs

9 years 13 days ago
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.
Uli Wagner
Added 01 Nov 2010
Updated 01 Nov 2010
Type Conference
Year 2003
Where SODA
Authors Uli Wagner
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