Associated primes of the second power of closed neighborhood ideals of graphs

2025/07/11 by Ha Thi Thu Hien, Hien, Ha Thi Thu, Thanh Vu +1 · 1 citation
Mathematics · #13C15 #13F55 #Algebraic Geometry and Number Theory #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2507.08777

openalex publication_date 2025/07/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study simple graphs for which the maximal homogeneous ideal is an associated prime of the second power of their closed neighborhood ideals. In particular, we show that such graphs must have diameter at most 6, and that those with diameter 2 must be vertex diameter-2-critical.

Citations

• Regularity of Powers and symbolic powers of edge ideals of cubic circulant graphs
• Dominance complexes, neighborhood complexes and combinatorial Alexander duals
• Algebraic implications of neighborhood hypergraphs and their transversal hypergraphs
• Dominating ideals and closed neighborhood ideals of graphs
• Closed Neighborhood Ideals of Finite Simple Graphs
• In the Shadows of a hypergraph: looking for associated primes of powers\n of squarefree monomial ideals
• Monomial ideals with large projective dimension
• Powers of sums and their homological invariants
• Saturation and associated primes of powers of edge ideals
• On the associated primes and the depth of the second power of squarefree monomial ideals
• Colorings of hypergraphs, perfect graphs, and associated primes of powers of monomial ideals
• Associated primes of monomial ideals and odd holes in graphs
• Embedded Associated Primes of Powers of Square-free Monomial Ideals

Cited by

• Barile-Macchia Resolutions and the closed neighborhood ideal

Related

• Saturation and associated primes of powers of edge ideals
• Asymptotic Growth of Associated Primes of Certain Graph Ideals
• Closed Neighborhood Ideals of Finite Simple Graphs
• Normality and associated primes of Closed neighborhood ideals and dominating ideals
• Dominating ideals and closed neighborhood ideals of graphs