MATH Seminar

Title: Induced and noninduced Ramsey numbers of $k$-partite, $k$-uniform hypergraphs
Seminar: Combinatorics
Speaker: Steve La Fleur of Emory University
Contact: Dwight Duffus, dwight@mathcs.emory.edu
Date: 2012-11-16 at 4:00PM
Venue: MSC W303
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Abstract: Given two (hyper)graphs $S$ and $T$, the Ramsey number $r(S,T)$ is the smallest integer $n$ such that, for any two-coloring of the edges of $K_n$ with red and blue, we can find a red copy of $S$ or a blue copy of $T$. Similarly, the induced Ramsey number, $r_{\mathrm{ind}}(S,T)$, is defined to be the smallest integer $N$ such that there exists a (hyper)graph $R$ with the following property: In any two-coloring of the edges of $R$ with red and blue, we can always find a red \emph{induced} copy of $S$ or a blue \emph{induced} copy of $T$. In this talk we will discuss bounds for $r(K^{(k)}_{t,\dots,t}, K_s^{(k)})$ where $K^{(k)}_{t,\dots,t}$ is the complete $k$-partite $k$-graph with partition classes of size $t$. We also present new upper bounds for $r_{\mathrm{ind}}(S, T)$, where $T \subseteq K^{(k)}_{t,\dots,t}$ and $S \subseteq K_s^{(k)}$.