Powers of edge ideals of regularity three bipartite graphs

TL;DR

This paper proves a precise formula for the regularity of powers of bipartite edge ideals with regularity three, revealing a linear pattern in their algebraic complexity.

Contribution

It establishes an exact regularity formula for all powers of bipartite edge ideals with initial regularity three, advancing understanding of their algebraic properties.

Findings

Regularity of I(G)^s is 2s+1 for all s ≥ 2

Confirms linear growth pattern in regularity of powers

Provides explicit regularity formula for a class of bipartite graphs

Abstract

In this paper we prove that if $I(G)$ is a bipartite edge ideal with regularity three then for all $s\geq 2$ the regularity of $I(G)^s$ is exactly $2s+1$.