A bound on degrees of primitive elements of toric graph ideals

TL;DR

This paper establishes an exponential upper bound on the degrees of primitive elements in toric graph ideals, linking it to the maximal degree of circuits, thus advancing understanding of their algebraic structure.

Contribution

It provides a new exponential bound on the degrees of primitive elements in toric graph ideals based on circuit degrees.

Findings

Degree of primitive elements is bounded exponentially by circuit degrees.

The bound improves understanding of the algebraic complexity of toric graph ideals.

Provides a theoretical framework for analyzing primitive elements in these ideals.

Abstract

We prove that for any toric ideal of a graph the degree of any element of Graver basis is bounded above by an exponential function of the maximal degree of a circuit.