Binomial edge ideals of bipartite graphs
Commutative Algebra
2017-05-09 v2 Combinatorics
Abstract
We classify the bipartite graphs whose binomial edge ideal is Cohen-Macaulay. The connected components of such graphs can be obtained by gluing a finite number of basic blocks with two operations. In this context we prove the converse of a well-known result due to Hartshorne, showing that the Cohen-Macaulayness of these ideals is equivalent to the connectedness of their dual graphs. We study interesting properties also for non-bipartite graphs and in the unmixed case, constructing classes of bipartite graphs with unmixed and not Cohen-Macaulay.
Cite
@article{arxiv.1704.00152,
title = {Binomial edge ideals of bipartite graphs},
author = {Davide Bolognini and Antonio Macchia and Francesco Strazzanti},
journal= {arXiv preprint arXiv:1704.00152},
year = {2017}
}