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Crossing Numbers and Hard Erdős Problems in Discrete Geometry

Published online by Cambridge University Press:  01 September 1997

Department of Mathematics, University of South Carolina, Columbia, SC 29208, USA (e-mail:


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.

Research Article
1997 Cambridge University Press

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