The Stable Set of Associated Primes of the Ideal of a Graph

By Janet Chen, Susan Morey, A-Young Sung. 2002

74 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/f85f0d6b9c322f2b1b43b2f8b816d333f0e8c597

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In Algebra and Number Theory

In Geometry and Topology

Citations in the corpus

Edge ideals: algebraic and combinatorial properties (2010, methodology): “This was done in [14], including a detailed explanation of how to work outward from multiple odd cycles.”
Blowup algebras of square-free monomial ideals and some links to combinatorial optimization problems (2006, background): “and combinatorial properties of edge ideals and graded algebras associated to graphs have been studied in [10, 20, 32, 33, 38].”
Bounds For Invariants of Edge-Rings (2005, unknown): “These rings and ideals have been studied by several authors: Chen et al. (2002), Simis (1990), Simis et al. (1994), Valencia (2003), Villarreal (1990, 1998), Vasconcelos (1994, Chapter 4), and Villarreal (2001, Chapter 6).”
Associated primes of powers of edge ideals (2011, unknown): “The set Ass(R/IN2) is nicely described in [17], and for edge ideals of graphs the set Ass(R/IN1) is described in [3].”
Embedded Associated Primes of Powers of Square-free Monomial Ideals (2008, methodology): “For example, edge ideals of odd cycles achieve this bound (see [2]).”
A Beginner’s Guide to Edge and Cover Ideals (2013, methodology): “For the case of the edge ideal, see the papers of Chen, Morey, and Sung [5] and Martinez-Bernal, Morey, and Villarreal [48].”
Depths of Powers of the Edge Ideal of a Tree (2009, background): “If G is a graph that is not bipartite, then G contains an odd cycle, and so by [5], ∈ Ass R/I for t >> 0.”
Persistence and stability properties of powers of ideals (2012, background): “This function has been first considered in [14] and subsequently for the edge ideals of a graph in [9].”