## Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

# Mittagsseminar (in cooperation with M. Ghaffari, A. Steger and B. Sudakov)

 Mittagsseminar Talk Information

Date and Time: Thursday, November 20, 2008, 12:15 pm

Duration: This information is not available in the database

Location: CAB G51

Speaker: Marek Sulovský

## Circle containment problem

The question is intuitively the following: given a set of n points in the plane, can one always choose two points a, b from P such that every disk D containing a and b contains many points of P, i.e. |D \cap P| >= tn + o(n) for some constant t. What is the maximum value c of this constant?

Edelsbunner et al. proved in 1989 that c > 1/4.7 but the proof was quite long and even worse, not completely correct. Although the mistake was fixed by later papers of Lovász et al.'04 and independently by Abrego et al.'05 the resulting proof of the lower bound is still quite complicated.

I will present a recent very short proof of this bound by P. Ramos and R. Viana from this year [paper].

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