  The $r$-size-Ramsey number $\hat{R}_r(H)$ of a graph $H$ is the smallest
number of edges a graph $G$ can have, such that for every edge-coloring of $G$
with $r$ colors there exists a monochromatic copy of $H$ in $G$. For a graph
$H$, we denote by $H^q$ the graph obtained from $H$ by subdividing its edges
with $q{-}1$ vertices each. In a recent paper of Kohayakawa, Retter and
R{\"o}dl, it is shown that for all constant integers $q,r\geq 2$ and every
graph $H$ on $n$ vertices and of bounded maximum degree, the $r$-size-Ramsey
number of $H^q$ is at most $(\log n)^{20(q-1)}n^{1+1/q}$, for $n$ large enough.
We improve upon this result using a significantly shorter argument by showing
that $\hat{R}_r(H^q)\leq O(n^{1+1/q})$ for any such graph $H$.
