  In a post on the Open Problems in Algebraic Combinatorics (OPAC) blog, E.
Bucher and J. Machacek posed three open problems: OPAC-033, OPAC-034, and
OPAC-035. These three problems deal with the relationships between three
infinite classes of quivers: the Banff, Louise, and $\mathcal{P}$ quivers.
OPAC-034 asks whether or not every Banff quiver can be verified to be Banff by
only considering sources and sinks, and OPAC-035 asks whether or not every
Banff quiver is contained in the class $\mathcal{P}$. We give an answer to both
questions, showing that every Banff quiver can be verified to be Banff by using
sources and sinks, and therefore that every Banff quiver lives in the class
$\mathcal{P}$. We also make some progress on OPAC-033, showing a result similar
to our result OPAC-034 for Louise quivers.
