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

Authors

  • Wafiq Hibi

Keywords:

The four-color theorem, chromatic number, planar graph, a clique in graph.

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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  2. Appel, W. Haken and J. Koch, (1977), Every planar map is four colorable. Part II. Reducibility, Illinois J. Math. 21,491–567.
  3. Robertson, D. P. Sanders,P. D. Seymour and R. Thomas, (1996). A new proof of the four-colour theorem, Electron.Res. Announc. AMS 2, 17–25.
  4. J,Mitchem.(1981). On the History and Solution of the Four-Color Map. The Two-Year College Mathematics Journal, Vol. 12, No. 2, pp. 108-116.
  5. Stojkovic, Natasa and Kocaleva, Mirjana and Martinovska, Cveta and Stojanova, Aleksandra and Zlatanovska, Biljana (2020) Application of the Four-Color Theorem for coloring a city map. Balkan Journal of Applied Mathematics and Informatics, 3 (1). pp. 25-36. ISSN 2545-480.

 

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Published

2022-02-01

How to Cite

Wafiq Hibi. (2022). The four-color theorem in the service of Euclidean distance Into the (n_0, ρ_0)-R^2 graphs. Yantu Gongcheng Xuebao/Chinese Journal of Geotechnical Engineering, 44(2), 1–4. Retrieved from http://ytgcxb.periodicales.com/index.php/CJGE/article/view/71

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Articles