Decreasing behavior of the depth functions of edge ideals

Ha Thi Thu Hien, Ha Minh Lam, Ngo Viet Trung

Let $I$ be the edge ideal of a connected non-bipartite graph and $R$ the base polynomial ring. Then $\mathrm{depth}R/I\ge 1$ and $\mathrm{depth}R/I^t=0$ for $t \gg…