A note on the circle containment problem
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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.
- 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.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.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
© Springer-Verlag New York Inc. 1989