# Complete colorings of planar graphs

## TL;DR

This paper investigates the maximum number of colors used in complete colorings of various classes of planar and surface-embedded graphs, providing tight bounds and asymptotic results.

## Contribution

It offers new asymptotic bounds and lower bounds for the achromatic and pseudoachromatic numbers of planar, outerplanar, and surface-embedded graphs.

## Key findings

- Asymptotically tight bounds for maximal embedded graphs.
- Lower bounds for achromatic and pseudoachromatic numbers.
- Results extend to graphs of girth 4 and on surfaces.

## Abstract

In this paper, we study the achromatic and the pseudoachromatic numbers of planar and outerplanar graphs as well as planar graphs of girth 4 and graphs embedded on a surface. We give asymptotically tight results and lower bounds for maximal embedded graphs.