Weak and strong Lefschetz properties for vertex cover Artinian algebras associated to graphs

Trung Chau, Tran Quang Hoa, Dang Thi Kieu Uyen

Let $G$ be a finite simple graph and let $A_c(G)$ be the Artinian algebra associated with its cover ideal. We prove that $A_c(G)$ has the WLP when $\tau (G)>|V(G)|/2$, where $\tau (G)$ den…