The sequentially Cohen-Macaulay property of edge ideals of edge-weighted graphs

Ly Thi Kieu Diem, Nguyen Cong Minh, Thanh Vu

Let $I(G_{\mathbf{w}})$ be the edge ideal of an edge-weighted graph $(G,\mathbf{w})$. We prove that $I(G_{\mathbf{w}})$ is sequentially Cohen-Macaulay for all weight functions $w$…