Crossing Numbers and Hard Erdős Problems in Discrete Geometry
Łászló A. Székely · Combinatorics Probability Computing · 1997
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.