Thanh Vu

activity

20222024

most citedDepth of powers of edge ideals of cycles and trees

2 citations · 3 across the 5 of their papers we have counts for

collaborators

Showing math.ACShow all

5 papers · 1 filter

math.AC2024

Projective dimension and regularity of 3-path ideals of unicyclic graphs

Nguyen Thu Hang, Thanh Vu

We compute the projective dimension and regularity of $3$ -path ideals of arbitrary graphs with at most one cycle.

math.AC2023

Depth of powers of edge ideals of Cohen-Macaulay trees

Nguyen Thu Hang, Truong Thi Hien, Thanh Vu

Let $I$ be the edge ideal of a Cohen-Macaulay tree of dimension $d$ over a polynomial ring $S = k [x_{1}, \dots, x_{d}, y_{1}, \dots, y_{d}]$ . We prove that for all $t \geq 1$ , $$\op…

math.AC2023

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

Ly Thi Kieu Diem, Nguyen Cong Minh, Thanh Vu

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

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★ 1 cited

Characterization of graphs whose a small power of their edge ideals has a linear free resolution

Nguyen Cong Minh, Thanh Vu

Let $I (G)$ be the edge ideal of a simple graph $G$ . We prove that $I (G)^{2}$ has a linear free resolution if and only if $G$ is gap-free and reg $I (G) \leq 3$ . Similarly, we show that…