2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/110177This is a survey of recently published results. We introduce and study a wide class algebras associated to directed graphs and related to factorizations of noncommutative polynomials. In particular, we show that for many well-known graphs such algebras are Koszul and compute their Hilbert series.To appear in Proceedings of the Conference "Lie Algebras, Vertex Operator Algebras and Their Applications"Rings and AlgebrasCombinatorics05E05; 15A15; 16W30text