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{\Large Department of Mathematics, BGU}

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{\Huge Combinatorics Seminar}\\[0.2\baselineskip]

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\textbf{On} \emph{Tuesday, April 30, 2019}
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\textbf{At} \emph{13:00 -- 14:00}
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\textbf{In} \emph{-101}

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{\large\scshape Minki Kim 
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will talk about
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{\Large\bfseries Rainbow independent sets in certain classes of graphs\par}
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\textsc{Abstract:}
Let \$F = (F\_1, \textbackslash{}ldots, F\_m)\$ be a collection of (not neccessarily distinct) sets.
A (partial) rainbow set for \$F\$ is a set of the form \$R = \{x\_\{i\_1\}, \textbackslash{}ldots, x\_\{i\_k\}\}\$ of distinct elements, where \$1 \textbackslash{}leq i\_1 \textless{} \textbackslash{}cdots \textless{} i\_k \textbackslash{}leq m\$ and \$x\_\{i\_j\}\$ is an element of \$F\_\{i\_j\}\$.
We are interested in the following question: given sufficiently many independent sets of size \$a\$ in a graph belonging to a certain class, there exists a rainbow independent set of size \$b\$.
In this talk, I will present our recent results on this question, mainly regarding \$H\$-(induced) free graphs and graphs of bounded maximum degree.
This is joint work with Ron Aharoni, Joseph Briggs and Jinha Kim.








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