Cohen-Macaulay generalized binomial edge ideals

Abstract

Let $G$ be a simple graph on $n$ vertices and let $J_{G,m}$ be the generalized binomial edge ideal associated to $G$ in the polynomial ring $K[x_{ij},1\le i\le m,1\le j\le n]$. We classify the Cohen-Macaulay generalized binomial edge ideals. Moreover we study the unmixedness and classify the bipartite and power cycle unmixed ones.