An algorithm for computing the universal Gr\"obner Basis of graph ideals

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