Lower bounds for the depth of second power of edge ideals

TL;DR

This paper establishes precise lower bounds on the depth of the square of a graph's edge ideal, linking algebraic properties to combinatorial graph invariants.

Contribution

It introduces sharp lower bounds for the depth of I(G)^2 based on the star packing number, connecting algebraic and combinatorial graph properties.

Findings

Sharp lower bounds for depth of I(G)^2

Connection between depth and star packing number

Enhanced understanding of edge ideal powers

Abstract

Assume that $G$ is a graph with edge ideal $I(G)$. We provide sharp lower bounds for the depth of $I(G)^2$ in terms of the star packing number of $G$.