We introduce a class of ideals generated by a set of -minors of an -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.
"The binomial edge ideal of a pair of graphs." Nagoya Math. J. 213 105 - 125, March 2014. https://doi.org/10.1215/00277630-2389872