  We study the rainbow version of the graph commonness property: a graph $H$ is
$r$-rainbow common if the number of rainbow copies of $H$ (where all edges have
distinct colors) in an $r$-coloring of edges of $K_n$ is maximized
asymptotically by independently coloring each edge uniformly at random. $H$ is
\emph{$r$-rainbow uncommon} otherwise. We show that if $H$ has a cycle, then it
is $r$-rainbow uncommon for every $r$ at least the number of edges of $H$. This
generalizes a result of Erd\H{o}s and Hajnal, and proves a conjecture of De
Silva, Si, Tait, Tun\c{c}bilek, Yang, and Young.
