  Cop-width and flip-width are new families of graph parameters introduced by
Toru\'nczyk (2023) that generalise treewidth, degeneracy, generalised colouring
numbers, clique-width and twin-width. In this paper, we bound the cop-width and
flip-width of a graph by its strong colouring numbers. In particular, we show
that for every $r\in \mathbb{N}$, every graph $G$ has $\text{copwidth}_r(G)\leq
\text{scol}_{4r}(G)$. This implies that every class of graphs with linear
strong colouring numbers has linear cop-width and linear flip-width. We use
this result to deduce improved bounds for cop-width and flip-width for various
sparse graph classes.
