6 papers
Depth of powers of integrally closed edge ideals of edge-weighted paths
Jiaxin Li, Thanh Vu, Guangjun Zhu
We compute the depth of powers of edge ideals of integrally closed edge-weighted paths.
Associated primes of the second power of closed neighborhood ideals of graphs
Ha Thi Thu Hien, Thanh Vu
We study simple graphs for which the maximal homogeneous ideal is an associated prime of the second power of their closed neighborhood ideals. In particular, we show that such grap…
Cochordal zero divisor graphs and Betti numbers of their edge ideals
Le Xuan Dung, Thanh Vu
We associate a sequence of positive integers, termed the type sequence, with a cochordal graph. Using this type sequence, we compute all graded Betti numbers of its edge ideal. We…
Normal edge ideals of edge-weighted graphs
Thanh Vu, Guangjun Zhu
We classify all normal edge ideals of edge-weighted graphs.
Regularity of integral closures of edge ideals of weighted oriented graphs
Nguyen Cong Minh, Thanh Vu, Guangjun Zhu
We prove that the regularity cannot increase when taking the integral closure for edge ideals of arbitrary weighted oriented graphs.
Regularity of linearly presented squarefree monomial ideals
Hailong Dao, Thanh Vu
We prove a sharp bound for the regularity of a squarefree monomial ideal with a linear presentation. This result also answers in positive a question on the cohomological dimension…