Normality of cut polytopes of graphs is a minor closed property

TL;DR

This paper proves that the property of a graph's cut polytope being normal is minor closed, advancing the understanding of Sturmfels-Sullivant's conjecture and simplifying the classes of graphs to consider.

Contribution

It establishes that normality of cut polytopes is minor closed, enabling broader classification and reducing the problem to 4-connected plane triangulations.

Findings

Normality of cut polytopes is minor closed.

Large classes of graphs with normal cut polytopes identified.

Focus can be narrowed to 4-connected plane triangulations for the conjecture.

Abstract

Sturmfels-Sullivant conjectured that the cut polytope of a graph is normal if and only if the graph has no K_5 minor. In the present paper, it is proved that the normality of cut polytopes of graphs is a minor closed property. By using this result, we have large classes of normal cut polytopes. Moreover, it turns out that, in order to study the conjecture, it is enough to consider 4-connected plane triangulations.