6 papers
On graphs whose powers are well-covered
My Hanh Pham, Thanh Vu
In this paper, we investigate graphs with the property that all of their powers are well-covered. We obtain complete classifications for several graph classes, including chordal gr…
Contractible independence complexes of trees
My Hanh Pham, Thanh Vu
We show that the independence complex of a tree is contractible if and only if it can be reduced to a path \( P_n \) with \( n \equiv 1 \pmod{3} \) by a sequence of truncation move…
Regularity of edge ideals of powers of graphs
My Hanh Pham, Thanh Vu
We prove that the regularity of edge ideals of powers of forests is weakly decreasing. We then compute the regularity of edge ideals of powers of cycles.
Unmixed and sequentially Cohen-Macaulay skew tableau ideals
Do Trong Hoang, Thanh Vu
We associate a {\it skew tableau ideal} to each filling of a skew Ferrers diagram with positive integers. We classify all unmixed and sequentially Cohen-Macaulay skew tableau ideal…
Regularity of normal Rees algebras of edge ideals of graphs
Cao Huy Linh, Quang Hoa Tran, Thanh Vu
We classify all graphs for which the Rees algebras of their edge ideals are normal and have regularity equal to their matching numbers.
Depth and regularity of tableau ideals
Do Trong Hoang, Thanh Vu
We compute the depth and regularity of ideals associated with arbitrary fillings of positive integers to a Young diagram, called the tableau ideals.