  This paper proves the following result: If $G$ is a planar graph and $L$ is a
$4$-list assignment of $G$ such that $|L(x) \cap L(y)| \le 2$ for every edge
$xy$, then $G$ is $L$-colourable. This answers a question asked by
Kratochv\'{i}l, Tuza and Voigt in [Journal of Graph Theory, 27(1):43--49,
1998].
