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SUMMARY:On the chromatic number of a sparse random hypergraph - Dmitry Sha
 banov (Moscow)
DTSTART:20171005T150000Z
DTEND:20171005T160000Z
UID:TALK86291@talks.cam.ac.uk
CONTACT:Andrew Thomason
DESCRIPTION:The talk deals with estimating the probability threshold for r
 -colorability of a random hypergraph. Let H(n\,k\,p) denote the classical 
 binomial model of a random k-uniform hypergraph: every edge of a complete 
 k-uniform hypergraph on n vertices is included into H(n\,k\,p) independent
 ly with probability p.\n\nWe study the question of estimating the probabil
 ity threshold for the r-colorability property of H(n\,k\,p). It is well kn
 own that for fixed r>=2 and $k>=2\, this threshold appears in the sparse c
 ase when the expected number of edges is a linear function cn for some fix
 ed c>0.\n\nWe will present a new lower bound for the r-colorability thresh
 old which improves previous result of Dyer\, Frieze and Greenhill (2015) a
 nd provides a bounded gap with the known upper bound. For the case r>>k\, 
 a slightly better result was recently obtained by Ayre\, Coja-Oghlan and G
 reenhill (2015+).\n\nThe proof of the main result is based on a new approa
 ch to the second moment method. We will also discuss the applications of t
 he used technique to the non-classical colorings of random hypergraphs.\n
LOCATION:MR12
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