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SUMMARY:Istvan Tomon (ETH Zurich)
DTSTART:20210503T140000Z
DTEND:20210503T150000Z
DTSTAMP:20260423T021142Z
UID:EPC/57
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/EPC/57/">Ram
 sey properties of string graphs</a>\nby Istvan Tomon (ETH Zurich) as part 
 of Extremal and probabilistic combinatorics webinar\n\n\nAbstract\nIn this
  talk\, I will give an outline of the proof of the following conjecture of
  Alon\, Pach\, Pinchasi\, Radoicic and Sharir. There exists an absolute co
 nstant $c>0$ such that any collection of $n$ curves (or in general arcwise
 -connected sets) in the plane contains a subset of size $n^c$ in which any
  two elements intersect\, or any two are disjoint. This generalizes many e
 arlier results about the Ramsey properties of intersection graphs of geome
 tric objects. The heart of our proof is a purely graph theoretic lemma\, w
 hich turned out to be quite useful in other Erdos-Hajnal type results as w
 ell\, see e.g. the recent proof of the Erdos-Hajnal conjecture for the cyc
 le of length 5 by Chudnovsky\, Scott\, Seymour and Spirkl. For this talk\,
  no knowledge of geometry is required.\n
LOCATION:https://researchseminars.org/talk/EPC/57/
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