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arXiv · 1203.2775

The binomial edge ideal of a pair of graphs

Viviana Ene·Jürgen Herzog·Takayuki Hibi·Ayesha Asloob Qureshi
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Abstract

We introduce a class of ideals generated by a set of 2-minors of $m\times n$-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 Gr\"obner basis and characterize unmixedness and Cohen--Macaulayness.

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Viviana Ene, Jürgen Herzog, Takayuki Hibi, Ayesha Asloob Qureshi. 2012-03-13. The binomial edge ideal of a pair of graphs. https://doi.org/10.1215/00277630-2389872

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