  A dominating set in a graph $G$ is a set $S$ of vertices such that every
vertex in $V(G) \setminus S$ is adjacent to a vertex in $S$. A restrained
dominating set of $G$ is a dominating set $S$ with the additional restraint
that the graph $G - S$ obtained by removing all vertices in $S$ is
isolate-free. The domination number $\gamma(G)$ and the restrained domination
number $\gamma_{r}(G)$ are the minimum cardinalities of a dominating set and
restrained dominating set, respectively, of $G$. Let $G$ be a cubic graph of
order~$n$. A classical result of Reed [Combin. Probab. Comput. 5 (1996),
277--295] states that $\gamma(G) \le \frac{3}{8}n$, and this bound is best
possible. To determine a best possible upper bound on the restrained domination
number of $G$ is more challenging, and we prove that $\gamma_{r}(G) \le
\frac{2}{5}n$.
