Geometric drawings of Kn with few crossings

We give a new upper bound for the rectilinear crossing number cr(n) of the complete geometric graph Kn. We prove that cr(n) ≤ 0.380559 ¡n 4 ¢ + Θ(n3 ) by means of a new construction based on an iterative duplication strategy starting with a set having a certain structure of halving lines.

• Type: Journal
• Year: 2007
• Where: JCT
• Authors: Bernardo M. Ábrego, Silvia Fernández-Merchant
• Keywords: Geometric Graph Kn, Iterative Duplication Strategy, JCT 2007, Rectilinear Crossing Number