# Wojciech Samotij "A sharp threshold for Ramsey's theorem"

**Wojciech Samotij** from Tel Aviv University will
give the talk "A sharp threshold for Ramsey's theorem" on the labs' Big Seminar.

Password: first 6 decimal places of $\pi$ after the decimal point

You can also write to Alexander Polyanskii (alexander.polyanskii@yandex.ru) or to Maksim Zhukovskii (zhukmax@gmail.com) if you want to be added to mailing list.

**Abstract:**

Given graphs $G$ and $H$ and an integer $r \ge 2$, we write $G \to (H)_r$ if every $r$-colouring of the edges of $G$ contains contains a monochromatic copy of $H$. It follows from Ramsey's theorem that, when $n$ is sufficiently large, $G \to (H)_r$ is a nontrivial, monotone property of subgraphs $G$ of $K_n$. The celebrated work of Rödl and Ruciński from the 1990s located the threshold for this property in the binomial random graph $G_{n,p}$ for all $H$ and $r$. We prove that this threshold is sharp when $H$ is a clique or a cycle, for every number of colours $r$; this extends earlier results of Friedgut, Rödl, Ruciński, and Tetali and of Schacht and Schulenburg.

This is joint work with Ehud Friedgut, Eden Kuperwasser, and Mathias Schacht.

Slides## Watch the video:

Everyone is invited to attend. The language of the lecture is English. The event is aimed at master and graduate students, as well as researchers in the field of combinatorics.