On approximately Cohen-Macaulay binomial edge ideal

Abstract

Binomial edge ideals IG of a graph G were introduced by [4]. They found some classes of graphs G with the property that IG is a Cohen-Macaulay ideal. This might happen only for few classes of graphs. A certain generalization of being Cohen-Macaulay, named approximately Cohen-Macaulay, was introduced by S. Goto in [3]. We study classes of graphs whose binomial edge ideal are approximately Cohen-Macaulay. Moreover we use some homological methods in order to compute their Hilbert series.

12 pages and 2 figures

Cited by in corpus (8)

• Extremal Betti numbers of some classes of binomial edge ideals
• The regularity of binomial edge ideals of graphs
• Weakly closed graphs and F-purity of binomial edge ideals
• On the regularity of binomial edge ideals
• Almost complete intersection binomial edge ideals and their Rees algebras
• On the Betti numbers of some classes of Binomial edge ideals
• Algebraic properties of binomial edge ideals of Levi graphs associated with curve arrangements
• Binomial edge ideals with pure resolutions