# A new lower bound on the maximum number of plane graphs using production matrices

## TL;DR

This paper introduces a new lower bound on the maximum number of crossing-free geometric graphs for certain point sets in the plane, using production matrices, surpassing previous bounds.

## Contribution

It applies production matrices to establish a higher lower bound of a6(42.11^n) for the number of such graphs, improving prior results.

## Key findings

- Established a lower bound of a6(42.11^n) for crossing-free geometric graphs
- Demonstrated the effectiveness of production matrices in combinatorial geometry
- Improved previous bounds from a6(41.18^n)

## Abstract

We use the concept of production matrices to show that there exist sets of $n$ points in the plane that admit $\Omega(42.11^n)$ crossing-free geometric graphs. This improves the previously best known bound of $\Omega(41.18^n)$ by Aichholzer et al. (2007).