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 $S=K[x_1,\dots ,x_n,y_1,\dots ,y_n].$ In this article, we prove that if $G$ is a fan graph of a complete graph, then $reg(S/J_G)\le c(G)$, where $c(G)$ denote the number of maximal cliques in $G$. Further, we show that if $G$ is a $k$-pure fan graph, then $reg(S/J_G)=k+1$. We then compute a precise expression for the regularity of Cohen-Macaulay bipartite graphs.

Minor correction in Remark 2.1; To Appear in Comm. Algebra

References in corpus (1)

• The regularity of binomial edge ideals of graphs

Cited by in corpus (1)

• Regularity of binomial edge ideals of chordal graphs