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SUMMARY:Lutz Warnke (Georgia Institute of Technology)
DTSTART:20200518T130000Z
DTEND:20200518T140000Z
DTSTAMP:20260404T164222Z
UID:EPC/5
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/EPC/5
 /">Counting extensions in random graphs</a>\nby Lutz Warnke (Georgia Insti
 tute of Technology) as part of Extremal and probabilistic combinatorics we
 binar\n\n\nAbstract\nWe consider rooted subgraphs in random graphs\, i.e.\
 , extension counts such as (a) the number of triangles containing a given 
 `root' vertex\, or (b) the number of paths of length three connecting two 
 given `root' vertices. \n\nIn 1989 Spencer gave sufficient conditions for 
 the event that\, whip\, all roots of the binomial random graph G(n\,p) hav
 e the same asymptotic number of extensions\, i.e.\, (1 \\pm \\epsilon) tim
 es their expected number. \n\nFor the important strictly balanced case\, S
 pencer also raised the fundamental question whether these conditions are n
 ecessary. \n\nWe answer this question by a careful second moment argument\
 , and discuss some intriguing problems that remain open.\n\nJoint work wit
 h Matas Sileikis\, see arXiv:1911.03012\n\nPassword: the first 6 prime num
 bers (8 digits in total)\n
LOCATION:https://stable.researchseminars.org/talk/EPC/5/
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