Graph-Chromatic Implicit Relations

TL;DR

This paper introduces a novel theoretical model for uncovering hidden implicit relations in graph coloring, which can be interpreted as unseen interactions or forces, and extends to NP-complete problems.

Contribution

It presents a new mathematical framework for implicit relations in graph coloring, with potential applications across various NP-complete problems.

Findings

Model of implicit-edges and implicit-identities introduced

Interpretation of relations as hidden forces or interactions

Extension to all NP-complete problems

Abstract

A theory about the implication structure in graph coloring is presented. Discovering hidden relations is a crucial activity in every scientific discipline. The development of mathematical models to study and discover such hidden relations is of the most highest interest. The main contribution presented in this work is a model of hidden relations materialized as implicit-edges and implicit-identities in the graph coloring problem, these relations can be interpreted in physical and chemical models as hidden forces, hidden interactions, hidden reactions or hidden variables. Also this theory can be extended to the complete class of NP-complete problems.