We show that w.h.p the list chromatic number $χ_\ell$ of the square of $G_{n,p}$ for $p=c/n$ is asymptotically equal to the maximum degree $Δ(G_{n,p})$. Since $χ(G^2_{n,p})\leq χ_\ell(G^2_{n,p})$, this also improves an earlier result of Garapaty et al \cite{KLMP} who proved that $χ(G^2_{n,p}) \leq 6 \cdot Δ(G_{n,p})$ w.h.p.
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