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SUMMARY:Tao Jiang (Miami University)
DTSTART:20200831T140000Z
DTEND:20200831T150000Z
DTSTAMP:20260423T035029Z
UID:EPC/21
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/EPC/21/">On 
 Turán exponents of graphs</a>\nby Tao Jiang (Miami University) as part of
  Extremal and probabilistic combinatorics webinar\n\n\nAbstract\nGiven a f
 amily of graphs ${\\mathcal F}$\, the Turán number $ex(n\,{\\mathcal F})$
  of ${\\mathcal F}$ is the maximum number of edges in an $n$-vertex graph 
 $G$ that does not contain any member of ${\\mathcal F}$ as a subgraph. In 
 a relatively recent breakthrough\, Bukh and Conlon verified a long-standin
 g conjecture in extremal graph theory that was credited to Erdős and Simo
 novits and re-iterated by other authors by showing that for every rational
  number $r$ between $1$ and $2$ there exists a family ${\\mathcal F}$ of g
 raphs such that $ex(n\,{\\mathcal F})=\\Theta(n^r)$.                      
                                                                           
                                                     \n\nThere is a stronge
 r conjecture that states that for every rational $r$ between $1$ and $2$ t
 here exists a single bipartite graph $F$ such that $ex(n\,F)=\\Theta(n^r)$
 . This conjecture is still open. In this talk\, we survey recent progress 
 on this stronger conjecture.\n
LOCATION:https://researchseminars.org/talk/EPC/21/
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