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CATEGORIES:Combinatorics and Probability Seminar
SUMMARY:The minimum number of triangles in a graph of give
n order and size - Katherine Staden (University of
Oxford)
DTSTART:20180220T150000Z
DTEND:20180220T160000Z
UID:TALK3080AT
URL:/talk/index/3080
DESCRIPTION:A famous theorem of Mantel from 1907 states that e
very n-vertex graph with more than n^2/4 edges con
tains at least one triangle. In the 50s\, Erdős as
ked for a quantitative version of this statement:
for every n and e\, how many triangles must an n-v
ertex e-edge graph contain? This question has rece
ived a great deal of attention\, and a long series
of partial results culminated in an asymptotic so
lution by Razborov\, extended to larger cliques by
Nikiforov and Reiher. Until recently\, an exact s
olution was only known for a small range of edge d
ensities\, due to Lovász and Simonovits. In this t
alk\, I will discuss the history of the problem an
d some new work which gives an exact solution for
almost the entire range of edge densities. This is
joint work with Hong Liu and Oleg Pikhurko.
LOCATION:Physics West 106
CONTACT:Allan Lo
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