Monomial cut ideals

TL;DR

This paper explores monomial cut ideals linked to graphs, revealing how their algebraic properties like primary decomposition and Cohen--Macaulayness depend on the graph's combinatorial structure.

Contribution

It establishes a connection between the algebraic properties of monomial cut ideals and the combinatorial features of the underlying graph.

Findings

Algebraic properties are derived from graph structure

Minimal primary decomposition characterized by graph features

Conditions for linear resolution and Cohen--Macaulayness identified

Abstract

B. Sturmfels and S. Sullivant associated to any graph a toric ideal, called the cut ideal. We consider monomial cut ideals and we show that their algebraic properties such as the minimal primary decomposition, the property of having a linear resolution or being Cohen--Macaulay may be derived from the combinatorial structure of the graph.