Hostname: page-component-848d4c4894-2pzkn Total loading time: 0 Render date: 2024-05-21T22:00:38.013Z Has data issue: false hasContentIssue false

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)