**Combinatorics and Computing Weekly Seminar**

On Ramsey Numbers Involving Berge Cycles

Leila Maherani, IPM

6 MAR 2024

14:00 - 15:00

For an arbitrary graph $G$, a hypergraph $mathcal{H}$ is called Berge-$G$ if there is an injection $i: V(G)longrightarrow V(mathcal{H})$ and a bijection $psi :E(G)longrightarrow E(mathcal{H})$ such that for each $e=uvin E(G)$, we have ${i(u),i(v)}subseteq psi (e)$. We denote by $mathcal{B}^rG$, the family of $r$-uniform Berge-$G$ hypergraphs. For families $mathcal{F}_1, mathcal{F}_2,ldots, mathcal{F}_t$ of $r$-uniform hypergraphs, the Ramsey number $R(mathcal{F}_1, mathcal{F}_2,ldots, mathcal{F}_t)$ is the minimum integer $n$ such that in every hyperedge coloring of the complete $r$-uniform hypergraph on $n$ vertices with $t$ colors, there exists $i$, $1leq ileq t$, such that there is a monochromatic copy of a hypergraph in $mathcal{F}_i$ of color $i$.In this lecture, we will first provide a brief history of Ramsey numbers and then focus on Ramsey numbers involving $3$-uniform Berge cycles.

Zoom room information:

https://us06web.zoom.us/j/89600366073?pwd=RMHt0eGdvGtkaDBG1Me3y8bOLgooGh.1 Meeting ID: 896 0036 6073

Passcode: 290109

**Venue**: Niavaran, Lecture Hall 1