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CATEGORIES:Combinatorics Seminar
SUMMARY:Minimising the Number of Triangles - Katherine Sta
den (University of Warwick)
DTSTART;TZID=Europe/London:20170518T143000
DTEND;TZID=Europe/London:20170518T153000
UID:TALK72266AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/72266
DESCRIPTION:A famous theorem of Mantel from 1907 states that e
very\n$n$-vertex graph with at least $n^2/4$ edges
contains at least one triangle. Erd\\H{o}s asked
for a quantitative version of this statement: for
every n and e\, how \\emph{many} triangles an must
an n-vertex e-edge graph contain? This question h
as received a great deal\nof attention\, and a lon
g series of partial results culminated in an asymp
totic solution by Razborov\, extended to larger cl
iques by Nikiforov and Reiher. Currently\, an exac
t solution is only known for a\nsmall range of edg
e densities\, due to Lov\\'asz and Simonovits. In
this talk\, I will discuss the history of the prob
lem and recent work which gives an exact solution
for almost the entire range of edge densities.\nTh
is is joint work with Hong Liu and Oleg Pikhurko.\
n
LOCATION:MR12
CONTACT:Andrew Thomason
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