The Universal Gröbner Basis of a Binomial Edge Ideal

  • Mourtadha Badiane
  • Isaac Burke
  • Emil Sköldberg
Keywords: Binomial edge ideals, Parity binomial edge ideals, Universal Gröbner basis, Graver basis


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.

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