Nagoya Mathematical Journal

The binomial edge ideal of a pair of graphs

Viviana Ene, Jürgen Herzog, Takayuki Hibi, and Ayesha Asloob Qureshi

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Abstract

We introduce a class of ideals generated by a set of 2-minors of an (m×n)-matrix of indeterminates indexed by a pair of graphs. This class of ideals is a natural common generalization of binomial edge ideals and ideals generated by adjacent minors. We determine the minimal prime ideals of such ideals and give a lower bound for their degree of nilpotency. In some special cases we compute their Gröbner basis and characterize unmixedness and Cohen–Macaulayness.

Article information

Source
Nagoya Math. J., Volume 213 (2014), 105-125.

Dates
First available in Project Euclid: 6 November 2013

Permanent link to this document
https://projecteuclid.org/euclid.nmj/1383747780

Digital Object Identifier
doi:10.1215/00277630-2389872

Mathematical Reviews number (MathSciNet)
MR3290687

Zentralblatt MATH identifier
1298.13020

Subjects
Primary: 13P10: Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) 13C13: Other special types
Secondary: 13C15: Dimension theory, depth, related rings (catenary, etc.) 13P25: Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.)

Citation

Ene, Viviana; Herzog, Jürgen; Hibi, Takayuki; Qureshi, Ayesha Asloob. The binomial edge ideal of a pair of graphs. Nagoya Math. J. 213 (2014), 105--125. doi:10.1215/00277630-2389872. https://projecteuclid.org/euclid.nmj/1383747780


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