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.
Categories: math.CO