Many toric ideals generated by quadratic binomials possess no quadratic Grobner bases

JOURNAL OF ALGEBRA

卷:408

Article

Hibi, Takayuki¹  Nishiyama, Kenta²  Ohsugi, Hidefumi³  Shikama, Akihiro¹ 

[1] Osaka Univ, Grad Sch Informat Sci & Technol, Dept Pure & Appl Math, Toyonaka, Osaka 5600043, Japan

[2] Univ Shizuoka, Sch Management & Informat, Suruga Ku, Shizuoka 4228526, Japan

[3] Rikkyo Univ, Coll Sci, Dept Math, Toshima Ku, Tokyo 1718501, Japan

关键词: Toric ideal;    Finite graph;    Grobner basis;   

DOI  :  10.1016/j.jalgebra.2013.09.039

来源: Elsevier

【 摘 要 】

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 IG possesses no quadratic Grobner 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. (c) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free