On the universal Gröbner bases of toric ideals of graphs

Details On the universal Gröbner bases of toric ideals of graphs On the universal Gröbner bases of toric ideals of graphs

2010-05-24

arxiv.org/abs/1005.4278v1

Mathematics

Commutative Algebra

11 pages, 5 figures

Scientific paper

The universal Gr\"{o}bner basis of $I$, is a Gr\"{o}bner 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 Gr\"{o}bner basis of the toric ideal $I_G$. We provide a bound for the degree of the binomials in the universal Gr\"{o}bner 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.

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