Graph Theory: The Four Coloring Theorem Essay -- Graph Geography Essay

graph Theory The quadruple Coloring Theorem Every planar mapping is iv colorable, seems like a pretty basic and easily provable statement. However, this unbiased concept took over one hundred years and involved much than a dozen mathematicians to finally prove it. Through by the century that many men pondered this idea, many otherwise problems, solutions, and mathematical concepts were created. I find the quatern Coloring Theorem to be very interesting because of its apparent simplicity diametric with its yen, laborious struggle to be proved. There is a very long and eventful history that accompanies this theorem. The concept of the Four Coloring Theorem was born in 1852 when Francis Guthrie noticed that he only needed iv different color in to color in a map of England. Through his brother, Frederick, Francis communicated his discovery to De Morgan. Francis wondered if De Morgan would be able to tell him if it was true or not. De Morgan was unsure, so he asked the said( prenominal) question to Hamilton in Dublin. Hamilton was unable to help, so De Morgan continued to ask other prominent mathematicians. In the US, Charles Peirce attempted to prove the Four Color hypothecate in the 1860s and continued to for the remainder of his life. In 1879, Cayley wrote a paper to the olympian Geographical Society explaining the difficulties in attempting to prove the Conjecture. On July 17, 1879, a mathematician by the name of Kempe announced a proof for the Four Color Conjecture. However, xi years later Heawood, a lecturer at Durham England, pointed out that Kempes proof was incorrect. Along with proving Kempe wrong, Heawood was able to prove that every planar map is five colorable. In 1898, Heawood also proved that if the number of edges around a region is... ...actually quite fun as well. They dont really have a real importance in the real world. The Four Color Theorem isnt firing to save any lives or catch life that much easier. However, it does make ma p coloring more simple by requiring only four colors. Bibliography (1) Fritsh, Rudolf and Gerda, The Four-Color Theorem, Springer-Verlag, New York, Inc., 1998. (2) Harary, Frank, Graph Theory, Adison-Wesley Publishing Co., Redding, MA, 1972, p.130-131. (3) Kainen, Paul, and Saaty, Thomas, The Four Color Problem, McGraw-Hill, Inc., Great Britain, 1977. (4) The Four Color Theorem, http//www-groups.dcs.st-and.ac.uk/history/HistTopics/The_four_colour_theorem.html, December 10, 1999. (5) The Four Color Theorem, Neil Robertson, Daniel P. Sanders, Paul Seymour, and robin Thomas, http//www.math.gatech.edu/thomas/FC/fourcolor.html, December 10, 1999.