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SUMMARY:Minimising the Number of Triangles - Katherine Staden (University 
 of Warwick)
DTSTART:20170518T133000Z
DTEND:20170518T143000Z
UID:TALK72266@talks.cam.ac.uk
CONTACT:Andrew Thomason
DESCRIPTION:A famous theorem of Mantel from 1907 states that every\n$n$-ve
 rtex 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 an
 d e\, how \\emph{many} triangles an must an n-vertex e-edge graph contain?
  This question has received a great deal\nof attention\, and a long series
  of partial results culminated in an asymptotic solution by Razborov\, ext
 ended to larger cliques by Nikiforov and Reiher. Currently\, an exact solu
 tion is only known for a\nsmall range of edge densities\, due to Lov\\'asz
  and Simonovits. In this talk\, I will discuss the history of the problem 
 and recent work which gives an exact solution for almost the entire range 
 of edge densities.\nThis is joint work with Hong Liu and Oleg Pikhurko.\n
LOCATION:MR12
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