Normality of cut polytopes of graphs is a minor closed property

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.

arXiv comment11 pages, References added, notation improved

References in corpus (1)

• Properties of cut ideals associated to ring graphs

Cited by in corpus (8)

• Multigraded Commutative Algebra of Graph Decompositions
• Gorenstein cut polytopes
• Retracts and algebraic properties of cut algebras
• Generalized Cut Polytopes for Binary Hierarchical Models
• Cut Polytopes of Minor-free Graphs
• A note on seminormality of cut polytopes
• The $h^{\ast }$-polynomial of the cut polytope of $K_{2,m}$ in the lattice spanned by its vertices
• Selected topics on Toric Varieties