Special Partial Graphs

TL;DR

This paper investigates specific minimal partial graphs with properties similar to planar triangulations, aiming to find new insights that could contribute to solving the Four Color Problem.

Contribution

It examines properties of minimal partial triangulations to explore their potential in proving the Four Color Problem.

Findings

Identified properties of special partial graphs

Potential connections to Four Color Problem

Foundation for future proof strategies

Abstract

The attempts to prove the Four Color Problem last for long years. A little hope arises that the properties of the minimal partial triangulations will be very useful for the solution of the Four Color Problem. That is why the material of this paper is devoted to the examination of the specific partial graphs and their properties. Such graphs will have all the elements of the planar triangulation, but will have the minimal size. And it will be quite interesting to found out their properties in order to search in the sequel for the possibility to prove the Four Color Problem on the base of their characteristics.