The binomial edge ideal of a pair of graphs

Details The binomial edge ideal of a pair of graphs The binomial edge ideal of a pair of graphs

2012-03-13

arxiv.org/abs/1203.2775v1

Mathematics

Commutative Algebra

Scientific paper

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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