Unmixed bipartite graphs and sublattices of the Boolean lattices

TL;DR

This paper explores the relationship between unmixed bipartite graphs and sublattices of Boolean lattices, demonstrating the existence of specific algebraic structures related to these graphs.

Contribution

It establishes a correspondence between unmixed bipartite graphs and sublattices of Boolean lattices, and shows the existence of squarefree quadratic initial ideals of toric ideals from minimal vertex covers.

Findings

Established a correspondence between graphs and lattice structures.

Proved existence of squarefree quadratic initial ideals for certain toric ideals.

Connected graph theory with algebraic geometry concepts.

Abstract

The correspondence between unmixed bipartite graphs and sublattices of the oolean lattice is discussed. By using this correspondence, we show the existence of squarefree quadratic initial ideals of toric ideals arising from minimal vertex covers of unmixed bipartite graphs.