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 2125000. 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.Comment: 13 pages, 2 figures + appendi