Bounding a global red-blue proportion using local conditions

Márton Naszódi, Leonardo Martínez-Sandoval, Shakhar Smorodinsky

Research output: Working paper/PreprintPreprint

Abstract

We study the following local-to-global phenomenon: Let B and R be two finite sets of (blue and red) points in the Euclidean plane R2 . Suppose that in each “neighborhood” of a red point, the number of blue points is at least as large as the number of red points. We show that in this case the total number of blue points is at least one fifth of the total number of red points. We also show that this bound is optimal and we generalize the result to arbitrary dimension and arbitrary norm using results from
Minkowski arrangements.
Original languageEnglish GB
PublisherarXiv:1701.02200 [cs.CG]
StatePublished - 20 Apr 2017

Keywords

  • Computer Science - Computational Geometry

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