Freiman cover ideals of unmixed bipartite graphs

Abstract

An equigenerated monomial ideal $I$ in the polynomial ring $R=k[z_1,\dots ,z_n]$ is a Freiman ideal if $\mu (I^2)=\ell (I)\mu (I)-\left(\genfrac{}{}{0ex}{}{\ell (I)}{2}\right)$ where $\ell (I)$ is the analytic spread of $I$ and $\mu (I)$ is the number of minimal generators of $I$. In this paper we classify all simple connected unmixed bipartite graphs whose cover ideals are Freiman ideals.