  In this note we consider a Ramsey property of random $d$-regular graphs,
$\mathcal{G}(n,d)$. Let $r\ge 2$ be fixed. Then w.h.p. the edges of
$\mathcal{G}(n, 2r)$ can be colored such that every monochromatic component has
size $o(n)$. On the other hand, there exists a constant $\gamma > 0$ such that
w.h.p., every $r$-coloring of the edges of $\mathcal{G}(n, 2r+1)$ must contain
a monochromatic cycle of length at least $\gamma n$. We prove an analogous
result for random $k$-out graphs.
