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\textsc{Combinatorics}
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\textsc{Seminar}
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\textit{Graphs on Affine or Linear Points}
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Hanno Lefmann\par

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\textbf{Abstract:} Motivated by a question of Hajnal on independent finite sum-sets in triangle-free graphs with vertex sets being the set of positive integers we consider the following problem:
Given are fixed integers k,l > 0 and a finite field F. Given is any  graph G = (V, E) with vertex set being the set of all affine or linear  points of an n-dimensional affine or linear vector space over F, where  G does not contain a complete graph on l vertices. Is it possible to  find a k-dimensional subspace, such that the set of all its affine or  linear points forms an independent set in G? Having answered this  questions, we give some applications to the corresponding problem for  the set of solutions of partition regular systems of linear equations  over Abelian groups. This is some joint work with D. Gunderson.\vspace{\fill}
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Friday, September 26, 2008, 4:00 pm\par
Mathematics and Science Center: W306
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\textsc{Mathematics and Computer Science}\par
\textsc{Emory University}
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