An algorithm for computing the universal Gröbner Basis of graph ideals

Abstract

The universal Gröbner basis of an ideal is a Gröbner basis with respect to all term orders simultaneously. The aim of this paper is to present an algorithmic approach to compute the universal Gröbner basis for the toric ideal corresponding to an undirected graph, based on the theoretical knowledge of this set and on a recent, efficiently computable algorithmic characterization of the Graver basis of the ideal.