Bounds on the regularity and projective dimension of ideals associated to graphs

2011/10/12 by Hailong Dao, Dao, Hailong, Craig Huneke +3 · 6 citations
Computer Science · Mathematics · #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1110.2570

openalex publication_date 2011/10/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we give new upper bounds on the regularity of edge ideals whose resolutions are k-steps linear; surprisingly, the bounds are logarithmic in the number of variables. We also give various bounds for the projective dimension of such ideals, generalizing other recent results. By Alexander duality, our results also apply to unmixed square-free monomial ideals of codimension two. We also discuss and connect these results to more classical topics in commutative algebra.

Citations

• Restricting linear syzygies: algebra and geometry

Cited by

• Linear resolution of connected graph ideals and their powers
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• Admissible set and squarefree-power-like function with applications to squarefree symbolic powers
• Comparing the v-number and h-polynomials of edge ideals
• Properties of LCM Lattices of Monomial Ideals

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