Genetic algorithm and edge-colorings of complete graphs with connected classes

TL;DR

This paper adapts a genetic algorithm to optimize the connected-pseudoachromatic index in complete graphs, achieving improved bounds and demonstrating the effectiveness of evolutionary methods in combinatorial graph theory.

Contribution

It introduces a novel application of the Rank Genetic Algorithm to a specific graph coloring problem, improving known bounds for the connected-pseudoachromatic index.

Findings

Improved bounds for the connected-pseudoachromatic index of complete graphs.

Demonstrated effectiveness of genetic algorithms in combinatorial optimization.

Validated the approach through computational experiments.

Abstract

In this study, the Rank Genetic Algorithm was adapted to address a problem in the field of Chromatic Graph Theory, namely, on the parameter called the connected-pseudoachromatic index. We successfully improved several previously known bounds of that index of the complete graph.