Cohen-Macaulay and Gorenstein path ideals of trees

Sara Saeedi Madani, Dariush Kiani

Let $R=k[x_1,\dots ,x_n]$, where $k$ is a field. The path ideal (of length $t\ge 2$) of a directed graph $G$ is the monomial ideal, denoted by $I_t(G)$, whose generators cor…