The four-color theorem in the service of Euclidean distance Into the (n_0, ρ_0)-R^2 graphs

Abstract

The four-color theorem in graph theory, [1,3 and 4] states that every planer graph is  - coloring (i.e., all the vertices of the graph can be colored in  colors in which no two vertices share the same edge have the same color).

In this paper, we will be based on this theorem, we will discover a feature in graphs, which are given in the Euclidean plane, and their edge are defined by Euclidean distances (see Theorem 1 and Theorem 2 in this paper).

REFERENCES

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