The binomial edge ideal of a pair of graphs

الأصل · EN

We introduce a class of ideals generated by a set of 2-minors of 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.