Some extremal results on circles containing points
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Abstract
We define Π(n) to be the largest number such that for every setP ofn points in the plane, there exist two pointsx, y ε P, where every circle containingx andy contains Π(n) points ofP. We establish lower and upper bounds for Π(n) and show that [n/27]+2≤Π(n)≤[n/4]+1. We define\(\bar \Pi (n)\) for the special case where then points are restricted to be the vertices of a convex polygon. We show that\(\bar \Pi (n) = [n/3] + 1\).
Keywords
Line Segment Bipartite Graph Discrete Comput Geom Convex Polygon Vertex Covering
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References
- 1.J. A. Bondy and U. S. R. Murty,Graph Theory with Applications, 74–75, 1976.Google Scholar
- 2.V. Neumann-Lara and J. Urrutia, A Combinatorial Result on Points and Circles on the Plane, Technical Report TR-85-15, University of Ottawa, 1985.Google Scholar
- 3.J. H. Schmerl, Private communication, University of Connecticut.Google Scholar
- 4.J. H. Schmerl, S. J. Sidney and J. Urrutia, A combinatorial result about points and balls in Euclidean space, preprint.Google Scholar
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© Springer-Verlag New York Inc 1989