# On line colorings of finite projective spaces

## TL;DR

This paper establishes bounds on the achromatic and pseudoachromatic indices of finite projective spaces, advancing understanding of their coloring properties in combinatorial geometry.

## Contribution

It provides new lower and upper bounds for these indices, which were previously unknown or less precise.

## Key findings

- Derived bounds improve existing knowledge of coloring indices.
- Results applicable to finite projective spaces of various dimensions and orders.
- Contributes to combinatorial geometry and graph coloring theory.

## Abstract

In this paper, we prove lower and upper bounds on the achromatic and the pseudoachromatic indices of the $n$-dimensional finite projective space of order $q$.