## Combinatorics Seminar - Spring '21

When: Sunday, May 8,
10am

Where: Schreiber 309

Speaker: Eden
Kuperwasser, Tel Aviv

Title:
The List-Ramsey Threshold

## Abstract:

Given a family of graphs $\mathcal{H}$ and an integer $r$, we say that a
graph is
$r$-Ramsey for $\mathcal{H}$ if any $r$-coloring of its edges admits a
monochromatic copy of a graph from $\mathcal{H}$. The threshold for the
classic
Ramsey problem, where $\mathcal{H}$ consists of one graph, was located in
the work
of R\"odl and Ruci\'nski.
In this talk we will offer a twofold generalization to this theorem:
showing that the list-coloring version of the property has the same
threshold, and extending this result for finite families $\mathcal{H}$.
This also
confirms further special cases of the Kohayakawa--Kreuter conjecture.

Joint with Wojciech Samotij.