  Let $G$ be a graph of minimum degree at least two with no induced subgraph
isomorphic to $K_{1,6}$. We prove that if $G$ is not isomorphic to one of eight
exceptional graphs, then it is possible to assign two-element subsets of
$\{1,2,3,4,5\}$ to the vertices of $G$ in such a way that for every
$i\in\{1,2,3,4,5\}$ and every vertex $v\in V(G)$ the label $i$ is assigned to
$v$ or one of its neighbors. It follows that $G$ has fractional domatic number
at least $5/2$. This is motivated by a problem in robotics and generalizes a
result of Fujita, Yamashita and Kameda who proved that the same conclusion
holds for all $3$-regular graphs.
