Minimal generators of toric ideals of graphs

TL;DR

This paper characterizes key types of binomials in the toric ideal of a graph using graph theory, providing a clearer understanding of their structure and properties.

Contribution

It offers a graph-theoretic characterization of primitive, minimal, indispensable, and fundamental binomials in toric ideals of graphs, advancing the theoretical understanding.

Findings

Characterization of primitive binomials in graph terms

Identification of minimal and indispensable binomials

Clarification of fundamental binomials in toric ideals

Abstract

Let $I_G$ be the toric ideal of a graph $G$. We characterize in graph theoretical terms the primitive, the minimal, the indispensable and the fundamental binomials of the toric ideal $I_G$.