The binomial edge ideal of a pair of graphs
Commutative Algebra
2015-01-14 v1 Combinatorics
Abstract
We introduce a class of ideals generated by a set of 2-minors of -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.
Keywords
Cite
@article{arxiv.1203.2775,
title = {The binomial edge ideal of a pair of graphs},
author = {Viviana Ene and Jürgen Herzog and Takayuki Hibi and Ayesha Asloob Qureshi},
journal= {arXiv preprint arXiv:1203.2775},
year = {2015}
}