Regularity of binomial edge ideals of Cohen-Macaulay bipartite graphs

Abstract

Let G be a finite simple graph on n vertices and J_G denote the corresponding binomial edge ideal in $S=K[x_1,\dots ,x_n,y_1,\dots ,y_n].$ We compute the Castelnuovo-Mumford regularity of $S/J_G$ when J_G is the binomial edge ideal of a Cohen-Macaulay bipartite graph. We achieve this by computing the regularity of certain bipartite subgraphs and some intermediate graphs, called k-fan graphs. In this process, we also obtain a class of graphs which satisfy the regularity conjecture of Saeedi Madani and Kiani.

Keywords:

• Binomial edge ideals
• Castelnuovo-Mumford regularity
• Cohen-Macaulay bipartite graph

MATHEMATICS SUBJECT CLASSIFICATION:

• 13D02
• 05E40

Acknowledgments

We have extensively used SAGE [9] and Macaulay 2 [5] for computational purposes.

Additional information

Funding

The second author thanks the National Board for Higher Mathematics, India for the financial support.