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Appel, Kenneth; Haken,Wolfgang, Every Planar Map is Four-Colorable, Providence, RI: American Mathematical Society. (1989).

has been cited by the following article:

Article

On Geometrical Methods that Provide a Short Proof of Four Color Theorem

1La Playa Street. 304. San Francisco.CA 94109, US


American Journal of Mathematical Analysis. 2015, Vol. 3 No. 3, 65-71
DOI: 10.12691/ajma-3-3-2
Copyright © 2015 Science and Education Publishing

Cite this paper:
BAHMAN MASHOOD. On Geometrical Methods that Provide a Short Proof of Four Color Theorem. American Journal of Mathematical Analysis. 2015; 3(3):65-71. doi: 10.12691/ajma-3-3-2.

Correspondence to: BAHMAN  MASHOOD, La Playa Street. 304. San Francisco.CA 94109, US. Email: b mashood@hotmail:com

Abstract

In this article we introduce a short and comprehensive proof of four color theorem based on geometrical methods. At the end of the article we will provide a short proof of the De Bruijn Erdos theorem for locally finite infinite graphs.

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