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   Seminário de Teoria da Computação e Combinatória (TCC)

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Título:      Bounding the maximum density of a 1-avoiding set 
             in the Euclidean plane

            
Palestrante: Fernando Mario Oliveira Filho
             Centrum voor Wiskunde en Informatica

Hora e Data: 14h, sexta-feira, 18 de março de 2011

Local:       auditório do NUMEC

Resumo:

A set of  points in the Euclidean plane  is 1-avoiding if no
two  points  in  the  set   lie  at  distance  1  from  each
other. What is the maximum fraction of the plane that can be
covered  by a  1-avoiding set?  Erdos conjectured  that less
than  1/4  of   the  plane  can  be  covered   with  such  a
set.  Together with  Frank Vallentin,  we provided  the best
known upper bound for this maximum density, 0.2684, which we
can even slightly improve now. I will discuss this question,
and give some ideas of how one would prove Erdos conjecture.