Stability of Depths of Powers of Edge Ideals

Abstract

Let $G$ be a graph and let $I:=I(G)$ be its edge ideal. In this paper, we provide an upper bound of $n$ from which $\depth R/ I(G)^n$ is stationary, and compute this limit explicitly. This bound is always achieved if $G$ has no cycles of length $4$ and every its connected component is either a tree or a unicyclic graph.

To appear in Journal of Algebra

References in corpus (1)

• On local cohomology of a tetrahedral curve

Cited by in corpus (7)

• Associated primes of powers of edge ideals and ear decompositions of graphs
• Powers of binomial edge ideals with quadratic Gröbner bases
• Stability of Depth and Cohen-Macaulayness of Integral Closures of Powers of Monomial Ideals
• Regularity of Powers of Unicyclic Graphs
• Stable value of depth of symbolic powers of edge ideals of graphs
• Stability of Associated Primes and Depth of Integral Closures of Powers of Edge Ideals
• The socle module of a monomial ideal