Mittagsseminar (in cooperation with J. Lengler, A. Steger, and D. Steurer)

Date and Time: Tuesday, March 02, 2021, 12:15 pm

Duration: 30 minutes

Location: Zoom: conference room

Speaker: Istvan Tomon

Ramsey properties of string graphs

A curve is the image of a continuous function from [0,1] to the plane. We prove that every set of n curves contains either n^c members that are pairwise disjoint, or n^c members that are pairwise intersecting, where c>0 is an absolute constant. This resolves a conjecture of Alon, Pach, Pinchasi, Radoičić and Sharir, also reiterated by Fox and Pach. Interestingly, the methods developed for the resolution of this problem played a key role in the recent breakthrough in the Erdős-Hajnal conjecture by Chudnovsky, Scott, Seymour and Spirkl.

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