# Levi’s Lemma, pseudolinear drawings of, and empty triangles.

Published:

Recommended citation: Arroyo, A., Bensmail, J. and Richter, R.B., 2018. Extending Drawings of Graphs to Arrangements of Pseudolines. arXiv preprint arXiv:1804.09317. https://arxiv.org/pdf/1804.09317.pdf

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 $K_n$ have $n^2+O(n\log n)$ and $O(n)$, respectively, empty triangles. All the arguments are elementary, algorithmic, and self-contained.