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TitleMany toric ideals generated by quadratic binomials possess no quadratic Gröbner bases
Author(s) Takayuki Hibi, Kenta Nishiyama, Hidefumi Ohsugi, Akihiro Shikama
TypeArticle in Journal
AbstractAbstract Let G be a finite connected simple graph and I G the toric ideal of the edge ring K [ G ] of G. In the present paper, we study finite graphs G with the property that I G is generated by quadratic binomials and I G possesses no quadratic Gröbner basis. First, we give a nontrivial infinite series of finite graphs with the above property. Second, we implement a combinatorial characterization for I G to be generated by quadratic binomials and, by means of the computer search, we classify the finite graphs G with the above property, up to 8 vertices.
KeywordsToric ideal, Finite graph, Gröbner basis
ISSN0021-8693
URL http://www.sciencedirect.com/science/article/pii/S0021869313005607
LanguageEnglish
JournalJournal of Algebra
Volume408
Pages138 - 146
Year2014
Edition0
Translation No
Refereed No
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