A Characterization of Gorenstein Planar graphs

TL;DR

This paper characterizes Gorenstein planar graphs by establishing that such graphs are precisely those whose independence complexes are Eulerian, providing a clear combinatorial criterion for Gorenstein property in planar graphs.

Contribution

It offers a complete characterization of Gorenstein planar graphs through the Eulerian property of their independence complexes, linking algebraic and topological graph properties.

Findings

Gorenstein planar graphs are characterized by Eulerian independence complexes.

The independence complex's Eulerian property is equivalent to the Gorenstein condition.

Provides a combinatorial criterion for identifying Gorenstein planar graphs.

Abstract

We prove that a planar graph is Gorenstein if and only if its independence complex is Eulerian.