Binomial Edge Ideals of Generalized block graphs

Abstract

We classify generalized block graphs whose binomial edge ideals admit a unique extremal Betti number. We prove that the Castelnuovo-Mumford regularity of binomial edge ideals of generalized block graphs is bounded below by $m(G)+1$, where $m(G)$ is the number of minimal cut sets of the graph $G$ and obtain an improved upper bound for the regularity in terms of the number of maximal cliques and pendant vertices of $G$.

Few examples, figures are added. Also, the proof of Theorem 4.5 has been corrected. Accepted for publication in International Journal of Algebra and Computation

References in corpus (1)

• Regularity of binomial edge ideals of chordal graphs

Cited by in corpus (1)

• Regularity of powers of quadratic sequences with applications to binomial ideals