A Partial Order on Bipartite Graphs with n Vertices

TL;DR

This paper explores a natural partial order on bipartite graphs with n vertices, relating to subobjects in a triangular category, providing a new perspective on their structural relationships.

Contribution

It introduces and analyzes a partial order on bipartite graphs within a categorical framework, linking graph theory with category theory concepts.

Findings

Defines a partial order on bipartite graphs with n vertices.

Connects the partial order to subobjects in a triangular category.

Provides structural insights into bipartite graph relationships.

Abstract

The paper examines a partial order on bipartite graphs (X1, X2, E) with n vertices, X1UX2={1,2,...,n}. This partial order is a natural partial order of subobjects of an object in a triangular category with bipartite graphs as morphisms.