Gorenstein Binomial Edge Ideals

TL;DR

This paper classifies connected graphs based on whether their binomial edge ideals are Gorenstein, using methods in prime characteristic to establish the classification.

Contribution

It provides a complete classification of connected graphs with Gorenstein binomial edge ideals, a novel result in algebraic combinatorics.

Findings

Identifies all connected graphs with Gorenstein binomial edge ideals

Uses prime characteristic methods for classification

Advances understanding of algebraic properties of graph ideals

Abstract

We classify connected graphs $G$ whose binomial edge ideal is Gorenstein. The proof uses methods in prime characteristic.