IPM Calendar 
Tuesday 21 May 2024   Today  
Events for day: Wednesday 06 March 2024    
           14:00 - 15:00     Combinatorics and Computing Weekly Seminar
On Ramsey Numbers Involving Berge Cycles

School
MATHEMATICS

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 $t$ c ...