Linear polynomial for the regularity of powers of edge ideals of very well-covered graphs

Abstract

Let $G$ be a finite simple graph and $I(G)$ denote the corresponding edge ideal. In this paper we prove that if $G$ is a very well-covered graph then for all $s\ge 2$ the regularity of $I(G{)}^s$ is exactly $2s+\nu (G)-1$.

Some of the proofs have been modified. Main results remain the same. To appear in Journal of Commutative Algebra

References in corpus (2)

• Betti Numbers of Graph Ideals
• On bounds for some graph invariants