Bounds on the regularity and projective dimension of ideals associated to graphs
By Hailong Dao, Craig Huneke, Jay Schweig. 2011
189 citations recorded by the source corpus.
In this paper, we give new upper bounds on the regularity of edge ideals whose resolutions are k-step 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.
Subfields: Algebra and Number Theory, Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/0277655b4db7cddd3573dc80238d939cadfc6056
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Algebra and Number Theory
In Computational Theory and Mathematics
Citations in the corpus
- Matchings, coverings, and Castelnuovo-Mumford regularity (2010, result): “d similar hardness results can be found in [25, Chapter 7]. 4.8. Questions on claw-free graphs. Nevo [29] showed that if G is a (2K2, claw)- free graph, then reg(R/I(G)) ≤ 2. Dao, Huneke, and Schweig [9] have recently given an alternate proof. Can the same be shown using Lemma 1? Question 23. If G i”
- The regularity of powers of edge ideals (2014, background): “1 of [1], which we shall use a lot in this work.”