Bounds for the regularity of product of edge ideals

Abstract

Let $I$ and $J$ be edge ideals in a polynomial ring $R=\mathbb{K}[x_1,\dots ,x_n]$ with $I\subseteq J$. In this paper, we obtain a general upper and lower bound for the Castelnuovo-Mumford regularity of $IJ$ in terms of certain invariants associated with $I$ and $J$. Using these results, we explicitly compute the regularity of $IJ$ for several classes of edge ideals. Let $J_1,\dots ,J_d$ be edge ideals in a polynomial ring $R$ with $J_1\subseteq \cdots \subseteq J_d$. Finally, we compute the precise expression for the regularity of $J_1{J}_2\cdots J_d$ when $d\in \{3,4\}$ and $J_d$ is the edge ideal of complete graph.

Pages 19, 3 figures, Accepted for publication in "Algebraic Combinatorics"

References in corpus (3)

• Castelnuovo-Mumford regularity of products of ideals
• Betti Numbers of Graph Ideals
• Powers of Ideals Associated to $(C_4,2K_2)$-free Graphs