6 papers · 1 filter
Depth and regularity of powers of edge ideals of edge-weighted trees
Truong Thi Hien, Jiaxin Li, Tran Nam Trung +1
For an increasing weighted tree , we obtain an asymptotic value and a sharp bound on the index stability of the depth function of its edge ideal . Moreover, if $G_Ï…
Cohen-Macaulayness of Powers of Edge Ideals of Weighted Oriented Graphs
Truong Thi Hien, Jiaxin Li, Tran Nam Trung +1
For the edge ideal $I(\D)$ of a weighted oriented graph $\D$, we prove that its symbolic powers $I(\D)^{(t)}$ are Cohen-Macaulay for all if and only if the underlyin…
Associated primes of powers of edge ideals of edge-weighted trees
Jiaxin Li, Tran Nam Trung, Guangjun Zhu
In this paper, we give a complete description of the associated primes of each power of the edge ideal of an increasing weighted tree.
Cohen-Macaulayness of powers of edge ideals of edge-weighted graphs
Jiaxin Li, Tran Nam Trung, Guangjun Zhu
In this paper, we characterize the Cohen-Macaulayness of the second power of the weighted edge ideal when the underlying graph is a very well-covered grap…
Stable value of depth of symbolic powers of edge ideals of graphs
Nguyen Cong Minh, Tran Nam Trung, Thanh Vu
Let be a simple graph on vertices. We introduce the notion of bipartite connectivity of , denoted by and prove that $$\lim_{s \to \infty} \operato…
A general formula for the index of depth stability of edge ideals
Ha Minh Lam, Ngo Viet Trung, Tran Nam Trung
By a classical result of Brodmann, the function is asymptotically a constant, i.e. there is a number such that $\operatorname{depth} R/I^t = \opera…