A New Method Based on Undirected Graph and Polygon Triangulation to Prove the Four-Color Theorem

Geng Xue; Hui Liu; Shi Xian Li; Wei Chen

doi:10.4028/www.scientific.net/AMM.347-350.2832

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HomeApplied Mechanics and MaterialsApplied Mechanics and Materials Vols. 347-350A New Method Based on Undirected Graph and Polygon...

A New Method Based on Undirected Graph and Polygon Triangulation to Prove the Four-Color Theorem

Abstract:

The development of computer science and plane geometry brings a new favorable opportunity for the research about the Four-color Theorem. After converting original map to undirected graph, this paper proposes a new method based on undirected graph and polygon triangulation to prove the Four-color Theorem.

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Periodical:

Applied Mechanics and Materials (Volumes 347-350)

Pages:

2832-2835

DOI:

https://doi.org/10.4028/www.scientific.net/AMM.347-350.2832

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Online since:

August 2013

Authors:

Geng Xue, Hui Liu, Shi Xian Li, Wei Chen

Keywords:

Four-Color Theorem, Polygon Triangulation, Undirected Graph

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References

[1] Ouyang Guangzhong. The Four-color Problem[M]. People Education Press. (1981).

Google Scholar

[2] K. May. The Origin of the Four- Color Conjecture[J]. Isis. 1965, 56, pp.346-348.

DOI: 10.1086/350003

Google Scholar

[3] Kempe A B. On the geographical problem of the four colors[J]. Amer J Math, 1879(2): 193-200.

Google Scholar

[4] A. Cayley. On the Colouring of Maps[J] . Proceedings of the Royal Geographical Society ( New Series) . 1879( 1) : 259- 261.

Google Scholar

[5] Appel K I, HakenW. Every planar map is four colourable [J ]. Bull. Am. M ath. Soc. 1976, 82: 711-712.

Google Scholar

[6] N. Robertson, D. Sanders, P. Seymour, R. Thomas. The Four- Color Theorem[J]. Journal of Combinatorial Theory (Ser. B) . 1997, 70: 2- 44.

Google Scholar

[7] G. Gonthier. Formal Proof: The Four- Color Theorem[J]. Notices of the AMS. 2008, 55( 11) : 1382- 1393.

Google Scholar

[8] T. Pavlidis. Algorithms for graphics and image processing[J]. Rockville, Computer Science, (1982).

Google Scholar

[9] Ma Xiaohu, Pan Zhigeng. Triangulation of simple polygon based on determination of convex concave vertices[J]. Journal of Computer-Aided Design & Computer Graphics, 1999, 11(1): 1-3.

Google Scholar

[10] Liu Qiang, Li Deren. A Recursive Algorithm for Triangulation of Arbitrary Polygons Based on BSP Tree[J]. Journal of Wuhan University (Information Science Edition), 2002, 27(5): 528-532.

Google Scholar

[11] Zhang Yuping, Jaing Shouwei. Efficient Approach of Convex Hull Triangulation Based on Monotonic Chain[J]. Journal of Nanjing University of Science and Technology, 2004, 28(6): 590-594.

Google Scholar

[12] Xue Geng, Fan Xiumei, Liao Lejian. The Application of Map-coloring Technology to Backbone Routing System[C]. Proceedings of the 2009 International Symposium on Computer Network and Multimedia Technology. CNMT 2009, pp.1136-9, (2009).

DOI: 10.1109/cnmt.2009.5374615

Google Scholar