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

DOI10.1016/j.jalgebra.2013.09.039zbMath1304.13040arXiv1302.0207OpenAlexW2964097306MaRDI QIDQ402702

Takayuki Hibi, Kenta Nishiyama, Hidefumi Ohsugi, Akihiro Shikama

Publication date: 28 August 2014

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1302.0207

zbMATH Keywords

Gröbner basistoric idealfinite graph

Mathematics Subject Classification ID

Polynomial rings and ideals; rings of integer-valued polynomials (13F20) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10)

Related Items (8)

Geometric vertex decomposition and liaison for toric ideals of graphs ⋮ Lexicographic and reverse lexicographic quadratic Gröbner bases of cut ideals ⋮ Linear flags and Koszul filtrations ⋮ Induced matching numbers of finite graphs and edge ideals ⋮ Quadratic-monomial generated domains from mixed signed, directed graphs ⋮ Betti numbers of toric algebras of certain bipartite graphs ⋮ Matching numbers and dimension of edge ideals ⋮ Toric ideals associated with gap-free graphs

Uses Software

• Macaulay2
• nauty
• Risa/Asir
• TiGERS

Cites Work

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• Regularity of edge ideals of \(C_{4}\)-free graphs via the topology of the lcm-lattice
• Algebraic properties of edge ideals via combinatorial topology
• Koszul bipartite graphs
• Toric ideals generalized by quadratic binomials
• Combinatorial pure subrings.
• \(C_{4}\)-free edge ideals
• Monomial and toric ideals associated to Ferrers graphs
• Rees algebras of edge ideals
• INDISPENSABLE BINOMIALS OF FINITE GRAPHS

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