  Lettericity is a graph parameter responsible for many attractive structural
properties. In particular, graphs of bounded lettericity have bounded linear
clique-width and they are well-quasi-ordered by induced subgraphs. The latter
property implies that any hereditary class of graphs of bounded lettericity can
be described by finitely many forbidden induced subgraphs. This, in turn,
implies, in a non-constructive way, polynomial-time recognition of such
classes. However, no constructive algorithms and no specific bounds on the size
of forbidden graphs are available up to date. In the present paper, we develop
an algorithm that recognizes $n$-vertex graphs of lettericity at most $k$ in
time $f(k)n^3$ and show that any minimal graph of lettericity more than $k$ has
at most $2^{O(k^2\log k)}$ vertices.
