The Universal Gröbner Basis of a Binomial Edge Ideal
Keywords:
Binomial edge ideals, Parity binomial edge ideals, Universal Gröbner basis, Graver basis
Abstract
We show that the universal Gröbner basis and the Graver basis of a binomial edge ideal coincide. We provide a description for this basis set in terms of certain paths in the underlying graph. We conjecture a similar result for a parity binomial edge ideal and prove this conjecture for the case when the underlying graph is the complete graph.