Bounded twin-width graphs are polynomially $\ddot{I}‡$-bounded

Romain Bourneuf, Stéphan Thomassé

We show that every graph with twin-width $t$ has chromatic number $O(\ddot{I}{‰}^{k_t})$ for some integer $k_t$, where $\ddot{I}‰$ denotes the clique number. This extends a quasi-polynomial bound…