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A graph $H$ is called {\\em chromatic-choosable} if $\\chi_l (H) = \\chi(H)$. It is an interesting problem to find graphs that are chromatic-choosable. A natural question raised by Xuding Zhu (2012) is whether there exists a constant integer $k$ such that $G^k$ is chromatic-choosable for every graph $G$. 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Let $\\chi(H)$ and $\\chi_l(H)$ be the chromatic number and the list chromatic number of $H$, respectively. A graph $H$ is called {\\em chromatic-choosable} if $\\chi_l (H) = \\chi(H)$. It is an interesting problem to find graphs that are chromatic-choosable. A natural question raised by Xuding Zhu (2012) is whether there exists a constant integer $k$ such that $G^k$ is chromatic-choosable for every graph $G$. 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