Powers of Ideals Associated to $(C_4,2K_2)$-free Graphs

Abstract

Let $G$ be a $(C_4,2K_2)$-free graph with edge ideal $I(G)\subset \mathbb{k}[x_1,\dots ,x_n]$. We show that $I(G{)}^s$ has linear resolution for every $s\ge 2$. Also, we show that every power of the vertex cover ideal of $G$ has linear quotients. As a result, we describe the Castelnuovo-Mumford regularity of powers of $I(G{)}^{\vee }$ in terms of the maximum degree of $G$.

revised to appear in Journal of Pure and Applied Algebra

References in corpus (1)

• Powers of Edge Ideals with Linear Resolutions

Cited by in corpus (7)

• Symbolic powers of edge ideals of graphs
• Ideals with componentwise linear powers
• Componentwise Linearity of Powers of Cover Ideals
• Relation between regularity of powers of edge ideals and (im, reg)-invariant extension
• Bounds for the regularity of product of edge ideals
• A new upper bound for the regularity of gap-free graphs
• Powers of facet ideals of simplicial trees