Freiman cover ideals of unmixed bipartite graphs

TL;DR

This paper classifies all simple connected unmixed bipartite graphs whose cover ideals are Freiman ideals, linking graph properties with algebraic structures of their ideals.

Contribution

It provides a complete classification of unmixed bipartite graphs with Freiman cover ideals, a novel connection between graph theory and algebra.

Findings

Classification of all such graphs achieved

Characterization of Freiman cover ideals in this class

Bridges between combinatorics and algebra established

Abstract

An equigenerated monomial ideal $I$ in the polynomial ring $R=k[z_1,\ldots, z_n]$ is a Freiman ideal if $\mu(I^2)=\ell(I)\mu(I)-{\ell(I)\choose 2}$ 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.