American Journal of Mathematical Analysis
ISSN (Print): 2333-8490 ISSN (Online): 2333-8431 Website: Editor-in-chief: Grigori Rozenblum
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American Journal of Mathematical Analysis. 2015, 3(3), 65-71
DOI: 10.12691/ajma-3-3-2
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On Geometrical Methods that Provide a Short Proof of Four Color Theorem


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Pub. Date: September 15, 2015

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


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.

four color theorem geometrical methods De Bruijn Erdos theorem

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[1]  Allaire, F, “Another proof of the four colour theoremPart I”, Proceedings, 7th Manitoba Conference on Numerical Mathematics and Computing, Congr. Numer. 20: 372. (1997).
[2]  Appel, Kenneth; Haken, Wolfgang, “Every Planar Map is Four Colorable Part I. Discharging”, Illinois Journal of Mathematics 21: 429490. (1977).
[3]  Appel, Kenneth; Haken, Wolfgang; Koch, John, “Every Planar Map is Four Colorable Part II. Reducibility”, Illinois Journal of Mathematics 21: 491567. (1977).
[4]  Appel, Kenneth; Haken, Wolfgang, “Solution of the Four Color Map Problem”, Scienti_c American 237 (4): 108121, (October 1977).
[5]  Appel, Kenneth; Haken,Wolfgang, Every Planar Map is Four-Colorable, Providence, RI: American Mathematical Society. (1989).
[6]  Bernhart, Frank R, “A digest of the four color theorem.”, Journal of Graph Theory 1: 207225, (1977).
[7]  Borodin, O. V, “Solution of the Ringel problem on vertex-face coloring of planar graphs and coloring of 1-planar graphs”, Metody Diskretnogo Analiza (41): 1226, 108, MR 832128. (1984).
[8]  Cayley, Arthur, “On the colourings of maps”, Proc. Royal Geographical Society (Blackwell Publishing) 1 (4): 259261, (1879).
[9]  Fritsch, Rudolf; Fritsch, Gerda, The Four Color Theorem: History, Topological Foundations and Idea of Proof, New York: Springer, (1998).
[10]  Gonthier, Georges, “Formal ProofThe Four-Color Theorem”, Notices of the American Mathematical Society 55 (11): 13821393, (2008).
[11]  Gonthier, Georges, A computer-checked proof of the four colour theorem, unpublished
[12]  (2005) Hadwiger, Hugo, “ber eine Klassi_kation der Streckenkom-plexe”, Vierteljschr. Naturforsch. Ges. Zrich 88: 133143. (1943).
[13]  Hale, Thomas C, The Jordan Curve Theorem formaly and informaly, The American Monthly 114(10):889-894.
[14]  Wilson, Richard and Newmann Victort Lara, Digital Jordan curves, Topology and its applications, Volume 46, Issued 3, 30 October (1992).
[15]  Tymchatyn,Ed,(Department of mathematics University of Saskatchewan), exchange of ideas and communications. (2014).