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.