Crossing numbers and hard Erdős problems in discrete geometry
László A. Székely
Department of Mathematics, University of South Carolina
Columbia SC 29208, USA
We show that an old but not well-known lower bound for the crossing number of a graph yields short proofs for a number of bounds in discrete plane geometry which were considered hard before: the number of incidences among points and lines, the maximum number of unit distances among n points, the minimum number of distinct distances among n points.