The chromatic class and the chromatic number of the planar conjugated triangulation

TL;DR

This paper investigates the chromatic number and class of planar conjugated triangulations, introduces new hypotheses related to the Four Color Problem, and explores their equivalence to it.

Contribution

It presents new hypotheses concerning the chromatic properties of conjugated triangulations and their potential equivalence to the Four Color Problem.

Findings

Proposes estimates for chromatic number and class of conjugated triangulations.

Introduces hypotheses that are equivalent to the Four Color Problem.

Explores properties of first and second conversions of planar triangulations.

Abstract

This material is dedicated to the estimation of the chromatic number and chromatic class of the conjugated triangulation (first conversion) and also of the second conversion of the planar triangulation. Also this paper introduces some new hypotheses, which are equivalent to Four Color Problem.