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Some extremal results on circles containing points (1989)

Hayward, Ryan ; Rappaport, David ; Wenger, Rephael

Springer

Discrete & computational geometry 4 (1989), S. 253-258

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ISSN: 1432-0444

Source: Springer Online Journal Archives 1860-2000

Topics: Computer Science , Mathematics

Notes: 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 $$\bar \Pi (n) = [n/3] + 1$$ .

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF02187726

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