Depth of powers of edge ideals of cycles and trees

2023/08/01 by Minh, Nguyen Cong, Trung, Tran Nam, Vu, Thanh · 2 citations
#13D02 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2308.00874

Abstract

Let I be the edge ideal of a cycle of length n ≥ 5 over a polynomial ring S = k[x₁,…,x_n]. We prove that for 2 ≤ t < \lceil (n+1)/2 \rceil, depth (S/I^t) = \lceil (n -t + 1)/(3) \rceil. When G = T_a is a starlike tree which is the join of k paths of length a₁, …, a_k at a common root 1, we give a formula for the depth of powers of I(T_a).

Cited by

• The vertex covers, Betti numbers and projective dimensions of perfect binary trees
• Depth of the 3-path Ideal of Square of a Path

Related

• Depth and Stanley depth of the edge ideals of the powers of paths and\n cycles
• Depth of powers of edge ideals of Cohen-Macaulay trees
• Depth and Stanley depth of powers of the path ideal of a cycle graph. II
• A Lower Bound For Depths of Powers of Edge Ideals
• Depth and Stanley depth of powers of the path ideal of a cycle graph