  For a given class ${\cal C}$ of graphs and given integers $m \le n$, let
$f_{\cal C}(n,m)$ be the minimal number $k$ such that every $k$ independent
$n$-sets in any graph belonging to ${\cal C}$ have a (possibly partial) rainbow
independent $m$-set. In this paper, we consider the case ${\cal
C}=\{C_{2s+1}\}$ and show that $f_{C_{2s+1}}(s, s) = s$. Our result is a
special case of the conjecture (Conjecture 2.9) proposed by Aharoni et al in
\cite{Aharoni}.
