  It is provided a local characterization of quasi-crystal graphs, by
presenting a set of local axioms, similar to the ones introduced by Stembridge
for crystal graphs of simply-laced root systems. It is also shown that
quasi-crystal graphs satisfying these axioms are closed under the tensor
product recently introduced by Cain, Guilherme and Malheiro. It is deduced that
each connected component of such a graph has a unique highest weight element,
whose weight is a composition, and it is isomorphic to a quasi-crystal graph of
semistandard quasi-ribbon tableaux.
