On the universal Gröbner bases of toric ideals of graphs |
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Authors: | Christos Tatakis Apostolos Thoma |
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Institution: | Department of Mathematics, University of Ioannina, Ioannina 45110, Greece |
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Abstract: | The universal Gröbner basis of an ideal is a Gröbner basis with respect to all term orders simultaneously. We characterize in graph theoretical terms the elements of the universal Gröbner basis of the toric ideal of a graph. We also provide a new degree bound. Finally, we give examples of graphs for which the true degrees of their circuits are less than the degrees of some elements of the Graver basis. |
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Keywords: | Toric ideals Toric varieties Graver basis Graphs Universal Grö bner bases Term orders |
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