  The weak degeneracy of a graph $G$ is a numerical parameter that was recently
introduced by the first two authors with the aim of understanding the power of
greedy algorithms for graph coloring. Every $d$-degenerate graph is weakly
$d$-degenerate, but the converse is not true in general (for example, all
connected $d$-regular graphs except cycles and cliques are weakly
$(d-1)$-degenerate). If $G$ is weakly $d$-degenerate, then the list-chromatic
number of $G$ is at most $d+1$, and the same upper bound holds for various
other parameters such as the DP-chromatic number and the paint number. Here we
rectify a mistake in a paper of the first two authors and give a correct proof
that planar graphs are weakly $4$-degenerate, strengthening the famous result
of Thomassen that planar graphs are $5$-list-colorable.
