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Turan Numbers of a Family of Graphs
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SpeakerProf. JIANG Tao     Miami University

Time2016-05-20 16:30-17:30

Place:1518

 

DetailGiven family L of graphs, the Turan number ex(n,L)  is defined to be the maximum number of edges in an n-vertex graph which does not contain  any member of L as a subgraph. In this talk, we study the Turan number of  the family of the graphs with  average degree at least d and order at most t  (denoted by  F_{d,t}) (d\geq 2). The case d=2 is equivalent tothe well-known girth problem. For ex(n, F_{d,t}), Random graphs give a lower bound on the order \Omega(n^{2-2/d). We give an almost matching upper bound of O(n^{2-2/d+c_{d,t}}) where c_{d,t} goes to 0 for fixed d as t goes to infinity . This partially answers a question of Verstraete.


 

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