  The induced $q$-color size-Ramsey number $\hat{r}_{\text{ind}}(H;q)$ of a
graph $H$ is the minimal number of edges a host graph $G$ can have so that
every $q$-edge-coloring of $G$ contains a monochromatic copy of $H$ which is an
induced subgraph of $G$. A natural question, which in the non-induced case has
a very long history, asks which families of graphs $H$ have induced Ramsey
numbers that are linear in $|H|$. We prove that for every $k,w,q$, if $H$ is an
$n$-vertex graph with maximum degree $k$ and treewidth at most $w$, then
$\hat{r}_{\text{ind}}(H;q) = O_{k,w,q}(n)$. This extends several old and recent
results in Ramsey theory. Our proof is quite simple and relies upon a novel
reduction argument.
