Discrete & Computational Geometry

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

A note on the circle containment problem

  • Ryan Hayward
Article

Abstract

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.

References

  1. 1.
    V. Neumann-Lara and J. Urrutia, A combinatorial result on points and circles in the plane, Technical Report TR-85-15, University of Ottawa, November 1985.Google Scholar
  2. 2.
    R. Hayward, D. Rappaport, and R. Wenger, Some extremal results on circles containing points,Discrete Comput. Geom., this issue, pp. 253–258.Google Scholar
  3. 3.
    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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