# Daniel Korandi "Exact stability for Turán's theorem"

**Daniel Korandi** from Oxford University will
give the talk "Exact stability for Turán's theorem" on the labs' Big Seminar.

Password: first 6 decimal places of $\pi$

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:**

Turán's theorem says that an extremal $K_{r+1}$-free graph is $r$-partite. The Stability Theorem of Erdös and Simonovits shows that if a $K_{r+1}$-free graph with $n$ vertices has close to the maximal $t_r(n)$ edges, then it is close to being r-partite. In this talk we determine exactly the $K_{r+1}$-free graphs with at least m edges that are farthest from being r-partite, for any $m > t_r(n) - δn^2$. This extends work by Erdös, Györi and Simonovits, and proves a conjecture of Balogh, Clemen, Lavrov, Lidický and Pfender. Joint work with Alexander Roberts and Alex Scott.

## 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.