  The size-Ramsey number $\hat r(G')$ of a graph $G'$ is defined as the
smallest integer $m$ so that there exists a graph $G$ with $m$ edges such that
every $2$-coloring of the edges of $G$ contains a monochromatic copy of $G'$.
Answering a question of Beck, Rodl and Szemeredi showed that for every $n\geq
1$ there exists a graph $G'$ on $n$ vertices each of degree at most three, with
the size-Ramsey number at least $cn\log^{\frac{1}{60}}n$ for a universal
constant $c>0$. In this note we show that a modification of Rodl and
Szemeredi's construction leads to a bound $\hat r(G')\geq cn\,\exp(c\sqrt{\log
n})$.
