Crossing Numbers and Hard Erdös Problems in Discrete Geometry

  • Authors:
  • László A. Székely

  • Affiliations:
  • Department of Mathematics, University of South Carolina, Columbia, SC 29208, USA (e-mail: laszlo@math.sc.edu)

  • Venue:
  • Combinatorics, Probability and Computing
  • Year:
  • 1997

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Abstract

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.