T. N. Trung

activity

20132025

most citedStable value of depth of symbolic powers of edge ideals of graphs

4 citations · 7 across the 10 of their papers we have counts for

collaborators

12 papers

math.AC2025

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 $G_{ω}$ , we obtain an asymptotic value and a sharp bound on the index stability of the depth function of its edge ideal $I (G_{ω})$ . Moreover, if $G_{ω}$ i…

math.AC2025

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 $t ⩾ 1$ if and only if the underlyin…

math.AC2025

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.

math.AC2025

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 $I (G_{ω})^{2}$ of the weighted edge ideal $I (G_{ω})$ when the underlying graph $G$ is a very well-covered graph.…

math.AC2023★ 4 cited

Stable value of depth of symbolic powers of edge ideals of graphs

Nguyen Cong Minh, Tran Nam Trung, Thanh Vu

Let $G$ be a simple graph on $n$ vertices. We introduce the notion of bipartite connectivity of $G$ , denoted by $bc (G)$ and prove that $$\lim_{s \to \infty} \operato…

math.AC2023★ 2 cited

Depth of powers of edge ideals of cycles and trees

Nguyen Cong Minh, Tran Nam Trung, Thanh Vu

Let $I$ be the edge ideal of a cycle of length $n \geq 5$ over a polynomial ring $S = k [x_{1}, \dots, x_{n}]$ . We prove that for $2 \leq t < ⌈(n + 1) /2 ⌉$ , $$\operatorna…

math.AC2022

Depth stability of cover ideals

Mai Phuoc Binh, Nguyen Thu Hang, Truong Thi Hien +1

Let R = K[x1,...,xr] be a polynomial ring over a field K. Let G be a graph with vertex set {1,...,r} and let J be the cover ideal of G. We give a sharp bound for the stability inde…

math.AC2021

Regularity of symbolic powers of square-free monomial ideals

Truong Thi Hien, Tran Nam Trung

We study the regularity of symbolic powers of square-free monomial ideals. We prove that if $I = I_{Δ}$ is the Stanley-Reisner ideal of a simplicial complex $Δ$ , then $\reg(I^{(n)})…

math.AC2021★ 1 cited

Stability of Associated Primes and Depth of Integral Closures of Powers of Edge Ideals

Dong Huu Mau, Tran Nam Trung

In this paper, we study associated primes and depth of integral closures of powers of edge ideals. We provide sharp bounds on how big of powers for which the set of associated prim…

math.AC2017

Regularity of powers of cover ideals of unimodular hypergraphs

Nguyen Thu Hang, Tran Nam Trung

Let $\H$ be a unimodular hypergraph over the vertex set $[n]$ and let $J () ˝$ be the cover ideal of $\H$ in the polynomial ring $R = K [x_{1}, \dots, x_{n}]$ . We show that $\reg J(\H)^s$ i…

math.AC2017

Regularity of symbolic powers and Arboricity of matroids

Nguyen Cong Minh, Tran Nam Trung

Let $Δ$ be a simplicial complex of a matroid $M$ . In this paper, we explicitly compute the regularity of all the symbolic powers of a Stanley-Reisner ideal $I_{Δ}$ in terms of combin…

math.AC2013

Combinatorial characterizations of the Cohen-Macaulayness of the second power of edge ideals

Do Trong Hoang, Nguyen Cong Minh, Tran Nam Trung

Let $I (G)$ be the edge ideal of a simple graph $G$ . In this paper, we will give sufficient and necessary combinatorial conditions of $G$ in which the second symbolic and ordinary p…