Generalizations of the Crossing Lemma

Abstract

The crossing number of a graph is the minimum number of crossings over all of its drawings on the plane. The Crossing Lemma, proved more than 40 years ago, is a tight lower bound on the crossing number of a graph in terms of the number of vertices and edges. It is definitely the most important inequality on crossing numbers. We review some generalizations and applications of the Crossing Lemma.

27 pages