Discrete & Computational Geometry

, Volume 4, Issue 3, pp 263–264 | Cite as

A note on the circle containment problem

  • Ryan Hayward


We extend a result due to Bárányet al. and prove the following theorem: given any setS ofn points in the plane, there are pointsx andy inS, such that every circle that containsx andy contains at least [5/84(n − 2)] other points ofS.


Euclidean Space Planar Graph Science Department Discrete Comput Geom Large Integer 
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    R. Hayward, D. Rappaport, and R. Wenger, Some extremal results on circles containing points,Discrete Comput. Geom., this issue, pp. 253–258.Google Scholar
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    I. Bárány, J. H. Schmerl, S. J. Sidney, and J. Urrutia, A combinatorial result about points and balls in Euclidean space,Discrete Comput. Geom., this issue, pp. 259–262.Google Scholar

Copyright information

© Springer-Verlag New York Inc. 1989

Authors and Affiliations

  • Ryan Hayward
    • 1
  1. 1.Computer Science DepartmentRutgers UniversityNew BrunswickUSA

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