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 $S = K[x_1, \ldots, x_n, y_1, \ldots, y_n].$ In this article, we prove that if $G$ is a fan graph of a complete graph, then $reg(S/J_G) \leq c(G)$, 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.
- Publication:
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arXiv e-prints
- Pub Date:
- June 2018
- DOI:
- 10.48550/arXiv.1806.02109
- arXiv:
- arXiv:1806.02109
- Bibcode:
- 2018arXiv180602109J
- Keywords:
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- Mathematics - Commutative Algebra
- E-Print:
- Minor correction in Remark 2.1