On a class of Koszul algebras associated to directed graphs

In [I. Gelfand, V. Retakh, S. Serconek, R.L. Wilson, On a class of algebras associated to directed graphs, Selecta Math. (N.S.) 11 (2005), math.QA/0506507] I. Gelfand and the authors of this paper introduced a new class of algebras associated to directed graphs. In this paper we show that these algebras are Koszul for a large class of layered graphs.