 
Summary: Geometric drawings of Kn with few crossings
Bernardo M. Ábrego, Silvia FernándezMerchant
California State University Northridge
{bernardo.abrego,silvia.fernandez}@csun.edu
ver 9
Abstract
We give a new upper bound for the rectilinear crossing number cr(n) of the complete geo
metric graph Kn. We prove that cr(n) 0.380559
ˇn
4
˘
+ (n3
) by means of a new construction
based on an iterative duplication strategy starting with a set having a certain structure of
halving lines.
Keywords: Rectilinear crossing number, crossing number, geometric graph, complete graph,
convex quadrilateral.
AMS Subject Classification: 05C62, 52A10, 52A22, 52C10.
1 Introduction
The crossing number cr (G) of a simple graph G is the minimum number of edge crossings in any
