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DESCRIPTION: In the theory of dense graph limits\, a graphon is a symmetric
measurable function W from [0\,1] ^2 to [0\,1]. Each graphon gives rise
naturally to a random graph distribution\, denoted G ( n \, W )\, that ca
n be viewed as a generalization of the Erdös-Rényi random graph. Recently\,
Dolezal\, Hladky\, and Mathe gave an asymptotic formula of order log n
for the size of the largest clique in G ( n \, W ) when W is bounded aw
ay from 0 and 1. We show that if W is allowed to approach 1 at a finite n
umber of points\, and displays a moderate rate of growth near these points\
, then the clique number of G ( n \, W ) will be of order √ n almost sure
ly. We also give a family of examples with clique number of order n ^ c
for any c in (0\,1)\, and some conditions under which the clique number
of G ( n \, W ) will be o (√ n ) or ω(√ n ). This talk assumes no previou
s knowledge of graphons.
DTSTAMP:20200120T074300
DTSTART:20200127T160000
CLASS:PUBLIC
LOCATION:Freie Universität Berlin \n Institut für Informatik \n Takustr. 9
\n 14195 Berlin \n Room 005 (Ground Floor)
SEQUENCE:0
SUMMARY:Gweneth Anne McKinley (MIT\, Cambridge\, USA): Super-logarithmic cl
iques in dense inhomogeneous random graphs
UID:104961232@www.facetsofcomplexity.de
URL:http://www.facetsofcomplexity.de/monday/20200127-C-McKinley.html
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