Gorenstein graphic matroids from multigraphs

TL;DR

This paper extends the classification of Gorenstein matroids, originally established for simple graphs, to include multigraphs, thereby broadening the understanding of their algebraic and combinatorial properties.

Contribution

It provides a comprehensive graph-theoretic classification of Gorenstein matroids associated with multigraphs, expanding previous work on simple graphs.

Findings

Extended classification to multigraphs

Identified new conditions for Gorenstein property

Broadened understanding of matroid toric varieties

Abstract

A matroid is Gorenstein if its toric variety is. Hibi, Laso\'n, Matsuda, Micha\l{}ek, and Vodi\v{c}ka provided a full graph-theoretic classification of Gorenstein matroids associated to simple graphs. We extend this classification to multigraphs.