# Géza Tóth "Disjointness graphs of short polygonal chains"

**Géza Tóth** from Alfréd Rényi Institute of Mathematics will
give the talk "Disjointness graphs of short polygonal chain" 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:**

The **disjointness graph** of a set system is a graph whose vertices
are the sets, two being connected by an edge if and only if they are disjoint.
It is known that the disjointness graph $G$ of any system of segments in
the plane is **$\chi$-bounded**, that is, its chromatic number $\chi(G)$
is upper bounded by a function of its clique number $\omega(G)$.

We show that this statement does not remain true for systems of polygonal chains of length $2$. Moreover, for polygonal chains of length $3$ the disjointness graph have arbitrarily large girth and chromatic number. We discuss some other, related results.

Joint work with János Pach and Gábor Tardos.

## 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.