T. N. Trung

activity

20132025

most citedDepth of powers of edge ideals of cycles and trees

2 citations · 3 across the 9 of their papers we have counts for

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12 papers · 1 filter

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

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…