  Laurent Phenomenon algebras, first introduced by Lam and Pylyavskyy, are a
generalization of cluster algebras that still possess many salient features of
cluster algebras. Linear Laurent Phenomenon algebras, defined by Lam and
Pylyavskyy, are a subclass of Laurent Phenomenon algebras whose structure is
given by the data of a directed graph. The main result of this paper is that
the cluster monomials of a linear Laurent Phenomenon algebra form a linear
basis, conjectured by Lam and Pylyavskyy and analogous to a result for cluster
algebras by Caldero and Keller.
