Binomial Edge Ideals with Quadratic Gröbner Bases

Marilena Crupi, Giancarlo Rinaldo


We prove that a binomial edge ideal of a graph $G$ has a quadratic Gröbner basis with respect to some term order if and only if the graph $G$ is closed with respect to a given labelling of the vertices. We also state some criteria for the closedness of a graph $G$ that do not depend on the labelling of its vertex set.

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