Open Access
March 2014 The binomial edge ideal of a pair of graphs
Viviana Ene, Jürgen Herzog, Takayuki Hibi, Ayesha Asloob Qureshi
Nagoya Math. J. 213: 105-125 (March 2014). DOI: 10.1215/00277630-2389872


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.


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Viviana Ene. Jürgen Herzog. Takayuki Hibi. Ayesha Asloob Qureshi. "The binomial edge ideal of a pair of graphs." Nagoya Math. J. 213 105 - 125, March 2014.


Published: March 2014
First available in Project Euclid: 6 November 2013

zbMATH: 1298.13020
MathSciNet: MR3290687
Digital Object Identifier: 10.1215/00277630-2389872

Primary: 13C13 , 13P10
Secondary: 13C15 , 13P25

Rights: Copyright © 2014 Editorial Board, Nagoya Mathematical Journal

Vol.213 • March 2014
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