Levi's Lemma, pseudolinear drawings of , and empty triangles

Abstract

Abstract There are three main thrusts to this article: a new proof of Levi's Enlargement Lemma for pseudoline arrangements in the real projective plane; a new characterization of pseudolinear drawings of the complete graph; and proofs that pseudolinear and convex drawings of have O and O( n 2 ), respectively, empty triangles. All the arguments are elementary, algorithmic, and self‐contained.