Details:
Title  Many toric ideals generated by quadratic binomials possess no quadratic Gröbner bases  Author(s)  Takayuki Hibi, Kenta Nishiyama, Hidefumi Ohsugi, Akihiro Shikama  Type  Article in Journal  Abstract  Abstract 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.  Keywords  Toric ideal, Finite graph, Gröbner basis  ISSN  00218693 
URL 
http://www.sciencedirect.com/science/article/pii/S0021869313005607 
Language  English  Journal  Journal of Algebra  Volume  408  Pages  138  146  Year  2014  Edition  0  Translation 
No  Refereed 
No 
