English

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 m×nm\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.

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}
}