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SUMMARY:Stability results for graphs containing a critical edge - Alexande
 r Roberts (University of Oxford)
DTSTART:20181108T143000Z
DTEND:20181108T153000Z
UID:TALK113137@talks.cam.ac.uk
CONTACT:Andrew Thomason
DESCRIPTION:The classical stability theorem of Erd\\H{o}s and Simonovits s
 tates that\, for any fixed graph $H$ with chromatic number $k+1 \\ge 3$\, 
 the following holds:\nevery $n$-vertex graph that is $H$-free and has with
 in $o(n 2)$ of the maximal possible number of edges can be made into the $
 k$-partite Tur\\'{a}n graph by adding and deleting $o(n 2)$ edges. We prov
 e sharper quantitative results for graphs $H$ with a critical edge\, showi
 ng how the $o(n 2)$ terms depend on each other. In many cases\, these resu
 lts are optimal to within a constant factor. We also discuss other recent 
 results in a similar vein and some motivation for providing tighter bounds
 .\n
LOCATION:MR12
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