English

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

Combinatorics 2015-11-24 v1 Geometric Topology

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 KnK_n have n2+n^2+{}O(nlogn)(n\log n) and O(n2)(n^2), respectively, empty triangles. All the arguments are elementary, algorithmic, and self-contained.

Keywords

Cite

@article{arxiv.1511.06808,
  title  = {Levi's Lemma, pseudolinear drawings of $K_n$, and empty triangles},
  author = {Alan Arroyo and Dan McQuillan and Bruce Richter and Gelasio Salazar},
  journal= {arXiv preprint arXiv:1511.06808},
  year   = {2015}
}