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   Seminário de Teoria da Computaçăo e Combinatória (TCC)

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Título:      Expansion, smoothness, and bipartite Turán numbers
            
Palestrante: Peter Allen
             London School of Economics and Political Science

Hora e Data: 14h50m, sexta-feira, 31 de agosto de 2012

Local:       Sala Multi-usos do Numec

Resumo:

Erdös and Simonovits conjectured  that for every family F of
bipartite  graphs, there  exists  k such  that the  extremal
number of edges in a bipartite F-free graph on n vertices is
asymptotically equal  to the extremal number of  edges in an
n-vertex  F-free graph  which  also avoids  the cycles  C_3,
C_5,...,  C_k.   We  describe  a general  approach  to  this
conjecture,  proving it for  'smooth families'  of bipartite
graphs, and in particular K_{2,t} and K_{3,3}.  Our approach
combines  Scott's   sparse  regularity  and   embedding  via
expansion.

This is joint work with Peter Keevash, Jacques Versträete
and Benny Sudakov.