  The hat guessing number is a graph invariant based on a hat guessing game
introduced by Winkler. Using a new vertex decomposition argument involving an
edge density theorem of Erd\H{o}s for hypergraphs, we show that the hat
guessing number of all outerplanar graphs is less than $2^{125000}$. We also
define the class of layered planar graphs, which contains outerplanar graphs,
and we show that every layered planar graph has bounded hat guessing number.
