radius-r flip-width – The radius-$r$ flip-width of a graph $G$, denoted $fwr (G)$, is the smallest number $k \in \mathbb{N}$ such that the cops have a winning strategy in the flipper game of radius $r$ and width $k$ on $G$
twin-width $k$ upper bounds radius-r flip-width by $2^{\mathcal O(k)}$ – Theorem 7.1. Fix $r \in \mathbb N$. For every graph $G$ of twin-width $d$ we have: $\mathrm{fw}_r(G) \le 2^d \cdot d^{O(r)}$.
