Depth and regularity of powers of edge ideals of edge-weighted trees

2025/09/10 by Hien, Truong Thi, Li, Jiaxin, Trung, Tran Nam +1
#05C05 #13C10 #Commutative Algebra (math.AC) #FOS: Mathematics #Primary 13C15 #Secondary 05E40

paper · doi:10.48550/arxiv.2509.08688

Abstract

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 is a strictly increasing weighted tree, we provide the minimal free resolution of I(G_ω) and an exact formula for the regularity of all powers of I(G_ω).

Citations

• Depth of powers of integrally closed edge ideals of edge-weighted paths
• Associated primes of powers of edge ideals of edge-weighted trees
• Cohen-Macaulayness of powers of edge ideals of edge-weighted graphs
• Depth of powers of edge ideals of edge-weighted integrally closed cycles
• Regularity of powers of edge ideals of edge-weighted integrally closed cycles
• Powers of edge ideals of edge-weighted trees
• Edge ideals of some edge-weighted graphs
• A general formula for the index of depth stability of edge ideals
• Linear polynomial for the regularity of powers of edge ideals of very well-covered graphs
• Regularity of powers of edge ideal of whiskered cycles
• A Lower Bound For Depths of Powers of Edge Ideals
• Regularity of powers of forests and cycles
• The projective dimension of sequentially Cohen-Macaulay monomial ideals
• The stable set of associated prime ideals of a polymatroidal ideal
• Depths of Powers of the Edge Ideal of a Tree
• Powers of Ideals and Fibers of Morphisms
• The depth of powers of an ideal
• Regularity jumps for powers of ideals
• Irrational Asymptotic Behaviour of Castelnuovo-Mumford Regularity

Related

• Powers of edge ideals of edge-weighted trees
• Edge ideals of some edge-weighted graphs
• Depths of Powers of the Edge Ideal of a Tree
• Regularity of powers of edge ideals of Cohen-Macaulay weighted oriented forests
• Depth of powers of integrally closed edge ideals of edge-weighted paths