  The hat guessing number of a graph is a parameter related to the hat guessing
game for graphs introduced by Winkler. In this paper, we show that graphs of
sufficiently large hat guessing number must contain arbitrary trees and
arbitrarily long cycles as subgraphs. More precisely, for each tree $T$, there
exists a value $N = N(T)$ such that every graph that does not contain $T$ as a
subgraph has hat guessing number at most $N$, and for each integer $c$, there
exists a value $N' = N'(c)$ such that every graph with no cycle of length
greater than $c$ has hat guessing number at most $N'$.
