# The de Bruijn-Erd\"os theorem in incidence geometry via Ph. Hall's marriage theorem

## TL;DR

This paper presents a novel proof of the de Bruijn-Erd"os theorem in incidence geometry utilizing Ph. Hall's marriage theorem, offering a new perspective on the theorem's foundational principles.

## Contribution

The paper introduces a proof of the de Bruijn-Erd"os theorem based on Hall's marriage theorem, connecting incidence geometry with combinatorial matching theory.

## Key findings

- Proof of de Bruijn-Erd"os theorem using Hall's marriage theorem
- Establishes a link between incidence geometry and combinatorial matching
- Provides a new methodological approach to the theorem

## Abstract

The paper is devoted to a proof of the de Bruijn-Erd\"os theorem in incidence geometry based on the Ph. Hall's marriage theorem (the theorem about the systems of distinct representatives).