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 Kn have n2+O(nlogn) and O(n2), respectively, empty triangles. All the arguments are elementary, algorithmic, and self‐contained.

No abstract

No abstract

No abstract

We present several general results about drawings of K n , as a beginning to trying to determine its crossing number. As application, we give a complete proof that the crossing number of K 9 is 36 and that all drawings in one large, natural class of drawings of K 11 have at least 100 crossings.