The Universal Gröbner Basis of a Binomial Edge Ideal

Mourtadha Badiane, Isaac Burke, Emil Sköldberg


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.


Binomial edge ideals; Parity binomial edge ideals; Universal Gröbner basis; Graver basis

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