On the universal Gröbner bases of toric ideals of graphs

Abstract

The universal Gröbner basis of $I$, is a Gröbner basis for $I$ with respect to all term orders simultaneously. Let $I_G$ be the toric ideal of a graph $G$. We characterize in graph theoretical terms the elements of the universal Gröbner basis of the toric ideal $I_G$. We provide a bound for the degree of the binomials in the universal Gröbner basis of the toric ideal of a graph. Finally we give a family of examples of circuits for which their true degrees are less than the degrees of some elements of the Graver basis.

arXiv comment11 pages, 5 figures

References in corpus (2)

• Minimal generators of toric ideals of graphs
• Equality of Graver bases and universal Gröbner bases of colored partition identities

Cited by in corpus (3)

• Generalized robust toric ideals
• Graver degrees are not polynomially bounded by true circuit degrees
• Ehrhart series for Connected Simple Graphs