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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.mi.fu-berlin.de
URL:https://www.mi.fu-berlin.de/en/facetsofcomplexity/monday/20200127-C-McK
 inley.html
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