The binomial edge ideal of a pair of graphs
Abstract
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 Gröbner basis and characterize unmixedness and Cohen--Macaulayness.
- Publication:
-
arXiv e-prints
- Pub Date:
- March 2012
- DOI:
- 10.48550/arXiv.1203.2775
- arXiv:
- arXiv:1203.2775
- Bibcode:
- 2012arXiv1203.2775E
- Keywords:
-
- Mathematics - Commutative Algebra;
- Mathematics - Combinatorics;
- 13P10;
- 13C13;
- 13C15;
- 13P25
- E-Print:
- Nagoya Math. J. 213 (2014), 105-125