Tag Archives: Geometric combinatorics

Coloring Problems for Arrangements of Circles (and Pseudocircles)

Posted on April 13, 2018 by Gil Kalai

To supplement and celebrate Aubrey de Grey’s result here are Eight problems on coloring circles A) Consider a finite family of unit circles. What is the minimum number of colors needed to color the circles so that tangent circles are … Continue reading →

Posted in Combinatorics, Geometry, Open problems | Tagged , , | 12 Comments

A Discrepancy Problem for Planar Configurations

Posted on February 3, 2010 by Gil Kalai

Yaacov Kupitz and Micha A. Perles asked: What is the smallest number C such that for every configuration of n points in the plane there is a line containing two or more points from the configuration for which the difference between the … Continue reading →

Posted in Combinatorics | Tagged , | 3 Comments

Extremal Combinatorics II: Some Geometry and Number Theory

Posted on July 17, 2008 by Gil Kalai

Extremal problems in additive number theory Our first lecture dealt with extremal problems for families of sets. In this lecture we will consider extremal problems for sets of real numbers, and for geometric configurations in planar Euclidean geometry. Problem I: Given a set A of … Continue reading →

Posted in Combinatorics, Open problems | Tagged , , | 6 Comments