Binomial Edge Ideals with Quadratic Gröbner Bases
Copyright policy )Binomial Edge Ideals with Quadratic Gröbner Bases
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.
- University of Trento Italy
- University of Messina Italy
Groebner bases; graphs, Structure, classification theorems for modules and ideals in commutative rings, Combinatorial aspects of simplicial complexes, Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), edge ideal, binomial ideal, Gröbner basis, Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.), Graphs and abstract algebra (groups, rings, fields, etc.)
Groebner bases; graphs, Structure, classification theorems for modules and ideals in commutative rings, Combinatorial aspects of simplicial complexes, Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), edge ideal, binomial ideal, Gröbner basis, Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.), Graphs and abstract algebra (groups, rings, fields, etc.)
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