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

graphical record Theory The quadruplet Coloring Theorem Every planar procedure is quaternion colorable, seems like a pretty basic and easily provable statement. However, this unbiased concept took over one hundred years and involved more than a dozen mathematicians to finally prove it. Through prohibited the century that umteen men pondered this idea, many early(a) problems, solutions, and mathematical concepts were created. I find the four-spot Coloring Theorem to be very interesting because of its apparent simplicity polar with its longsighted, 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 quadruplet different colour 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 selfsame(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 scheme in the 1860s and continued to for the remainder of his life. In 1879, Cayley wrote a paper to the purplish 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, cardinal 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 issue to save any lives or pos it life that much easier. However, it does make map 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.