Yelena Yuditsky (Université libre de Bruxelles): On Multicolour Ramsey Numbers

Abstract:
For $n\geq s> r\geq 1$ and $k\geq 2$, write $n \erarrow
(s)_{k}^r$ if every hyperedge colouring with $k$ colours of the complete
$r$-uniform hypergraph on $n$ vertices has a monochromatic subset of
size $s$. Improving upon previous results by Axenovich et al. and
Erd\H{o}s et al. we show that\[
\text{if } r \geq 3 \text{ and } n \nerarrow (s)_k^r \text{ then } 2^n
\nerarrow (s+1)_{k+3}^{r+1}.
\]
This improves some of the known lower bounds on multicolour hypergraph
Ramsey numbers.

This is a joint work with Bruno Jartoux, Chaya Keller and Shakhar
Smorodinsky.

Zoom link: https://zoom.us/j/2961946869