In the mathematics of graph drawing, the crossing number inequality or crossing lemma gives a lower bound on the minimum number of crossings of a given graph, as a function of the number of edges and vertices of the graph. It states that, for graphs where the number e of edges is sufficiently larger than the number n of vertices, the crossing number is at least proportional to e3/n2. It has applications in VLSI design and combinatorial geometry,and was discovered independently by Ajtai, Chvátal, Newborn, and Szemerédiand by Leighton.