# On the achromatic number of signed graphs

## TL;DR

This paper extends the concepts of complete coloring and achromatic number to signed and 2-edge-colored graphs, establishing relationships and proving NP-completeness of their computation.

## Contribution

It introduces generalized definitions for achromatic numbers in signed graphs and explores their computational complexity.

## Key findings

- Relationships between different definitions of achromatic numbers
- Proved NP-completeness of computing these numbers
- Extended classical concepts to signed and 2-edge-colored graphs

## Abstract

In this paper, we generalize the concept of complete coloring and achromatic number to 2-edge-colored graphs and signed graphs. We give some useful relationships between different possible definitions of such achromatic numbers and prove that computing any of them is NP-complete.