
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.
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Taxonomy
TopicsGraph Labeling and Dimension Problems · Advanced Graph Theory Research · graph theory and CDMA systems
