Buchsbaumness of the second powers of edge ideals

TL;DR

This paper provides a graph-theoretic characterization of graphs whose edge ideals' second powers are Buchsbaum, linking algebraic properties to combinatorial structures.

Contribution

It introduces a novel graph-theoretic criterion for identifying when the square of an edge ideal is Buchsbaum, advancing the understanding of algebraic properties via combinatorics.

Findings

Characterization of graphs with Buchsbaum second powers of edge ideals

Connection established between graph properties and algebraic Buchsbaumness

Provides tools for identifying Buchsbaum properties in graph-based ideals

Abstract

We graph-theoretically characterize the class of graphs $G$ such that $I(G)^2$ are Buchsbaum.