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SUMMARY:Annika Heckel (LMU Munich)
DTSTART:20200622T130000Z
DTEND:20200622T140000Z
DTSTAMP:20260423T052331Z
UID:EPC/11
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/EPC/11/">Non
 -concentration of the chromatic number</a>\nby Annika Heckel (LMU Munich) 
 as part of Extremal and probabilistic combinatorics webinar\n\n\nAbstract\
 nThere are many impressive results asserting that the chromatic number of 
 a random graph is sharply concentrated. In 1987\, Shamir and Spencer showe
 d that for any function p=p(n)\, the chromatic number of G(n\,p) takes one
  of at most about $n^{1/2}$ consecutive values whp. For sparse random grap
 hs\, much sharper concentration is known to hold: Alon and Krivelevich pro
 ved two point concentration whenever $p < n^{-1/2-\\varepsilon}$.\n\nHowev
 er\, until recently no non-trivial lower bounds for the concentration were
  known for any p\, even though the question was raised prominently by Erd
 ős in 1992 and by Bollobás in 2004.\n\nIn this talk\, we show that the c
 hromatic number of G(n\, 1/2) is not whp contained in any sequence of inte
 rvals of length $n^{1/2-o(1)}$\, almost matching Shamir and Spencer's uppe
 r bound.\n\nJoint work with Oliver Riordan.\n
LOCATION:https://researchseminars.org/talk/EPC/11/
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