Combinatorica

, Volume 35, Issue 1, pp 95–126 | Cite as

The Szemerédi-Trotter theorem in the complex plane

Original paper

Abstract

It is shown that n points and e lines in the complex Euclidean plane ℂ2 determine O(n 2/3 e 2/3 + n + e) point-line incidences. This bound is the best possible, and it generalizes the celebrated theorem by Szemerédi and Trotter about point-line incidences in the real Euclidean plane ℝ2.

Mathematics Subject Classication (2000)

05D99 52C35 

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Copyright information

© János Bolyai Mathematical Society and Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of MathematicsCalifornia State University NorthridgeLos AngelesUSA
  2. 2.Department of Computer ScienceTufts UniversityMedfordUSA

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