Associated primes of powers of edge ideals

By José Martínez-Bernal, Susan Morey, Rafael H. Villarreal. Collectanea Mathematica, 2011

106 citations recorded by the source corpus.

Let G be a graph and let I be its edge ideal. Our main result shows that the sets of associated primes of the powers of I form an ascending chain. It is known that the sets of associated primes of Ii and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\overline{I^i}}$$\end{document} stabilize for large i. We show that their corresponding stable sets are equal. To show our main result we use a classical result of Berge from matching theory and certain notions from combinatorial optimization.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/31f8032405c7e6974078b4ac476d4552f0a6a1f9

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Citations in the corpus

The stable set of associated prime ideals of a polymatroidal ideal (2011, background): “ open, even for monomial ideals, though in several interesting special cases, including edge ideals and vertex cover ideals, these questions have been answered quite comprehensively, see [5], [9] and [17]. A nice survey on what is known about the stability of associated prime ideals of powers of edg”
A Beginner’s Guide to Edge and Cover Ideals (2013, methodology): “The paper [48] is a good example of using results from graph theory to prove an interesting algebraic result.”
Persistence and stability properties of powers of ideals (2012, methodology): “Following [12] and [17] we define the index of stability for the associated prime ideals of the powers of I to be the number”