Speaker
Joonkyung Lee
(Hanyang University)
Description
A family $\mathcal{H}$ of graphs is said to be $\chi$-bounded, if there is a function $f:\mathbb{N}\rightarrow\mathbb{N}$ such that for every graph $H\in\mathcal{H}$ the chromatic number $\chi(H)$ of $H$ is at most $f(\omega)$, where $\omega$ is the clique number of $H$. We show that the family of graphs that do not have a cycle with exactly $k$ chords is $\chi$-bounded, for every large enough $k$. This proves a conjecture of Aboulker and Bousquet (2015) for sufficiently large $k$. Joint work with Shoham Letzter and Alexey Pokrovskiy.
