MIT Combinatorics Seminar

Ramsey-Type Results for Intersection Graphs

Jacob Fox (Massachusetts Institute of Technology)

Wednesday, May 3, 2006   4:30 PM   Building 2 Room 105 


Suppose we have a collection of $n$ curves in the plane. How large a subcollection can we necessarily find such that either every pair of curves in the subcollection pairwise intersects or every pair of curves in the subcollection are pairwise disjoint? The qualitative answer is, ``quite large.'' We will discuss how to employ different algebraic, combinatorial, geometric, and topological methods to tackle this problem and several variants of it. Along the way, we will come across several old and new conjectures in combinatorial geometry.

The talk is based on joint work with Janos Pach.