A lower bound for the Graver complexity of the incidence matrix of a complete bipartite graph

TL;DR

This paper establishes an exponential lower bound on the Graver complexity for the incidence matrix of complete bipartite graphs of any size, extending previous results for specific cases.

Contribution

It generalizes the known lower bounds for Graver complexity from small bipartite graphs to arbitrary sizes, providing a broader theoretical understanding.

Findings

Exponential lower bound for Graver complexity established

Generalization of previous bounds for 3xr bipartite graphs

Extends theoretical understanding of incidence matrices

Abstract

We give an exponential lower bound for the Graver complexity of the incidence matrix of a complete bipartite graph of arbitrary size. Our result is a generalization of the result by Berstein and Onn (2009) for 3xr complete bipartite graphs, r \ge 3.