  Weak degeneracy is a variation of degeneracy which shares many nice
properties of degeneracy. In particular, if a graph $G$ is weakly
$d$-degenerate, then for any $(d + 1)$-list assignment $L$ of $G$, one can
construct an $L$-coloring of $G$ by a modified greedy coloring algorithm. It is
known that planar graphs of girth 5 are 3-choosable and locally planar graphs
are 5-choosable. This paper strengthens these results and proves that planar
graphs of girth 5 are weakly 2-degenerate and locally planar graphs are weakly
4-degenerate.
