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CATEGORIES:Combinatorics Seminar
SUMMARY:On the chromatic number of a sparse random hypergr
aph - Dmitry Shabanov (Moscow)
DTSTART;TZID=Europe/London:20171005T160000
DTEND;TZID=Europe/London:20171005T170000
UID:TALK86291AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/86291
DESCRIPTION:The talk deals with estimating the probability thr
eshold 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 in
cluded into H(n\,k\,p) independently with probabil
ity p.\n\nWe study the question of estimating the
probability threshold for the r-colorability prope
rty of H(n\,k\,p). It is well known that for fixed
r>=2 and $k>=2\, this threshold appears in the sp
arse case when the expected number of edges is a l
inear function cn for some fixed c>0.\n\nWe will p
resent a new lower bound for the r-colorability th
reshold which improves previous result of Dyer\, F
rieze and Greenhill (2015) and provides a bounded
gap with the known upper bound. For the case r>>k\
, a slightly better result was recently obtained b
y Ayre\, Coja-Oghlan and Greenhill (2015+).\n\nThe
proof of the main result is based on a new approa
ch to the second moment method. We will also discu
ss the applications of the used technique to the n
on-classical colorings of random hypergraphs.\n
LOCATION:MR12
CONTACT:Andrew Thomason
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