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

Graph Theory The Four Coloring Theorem Every planar map is four colorable, seems like a pretty basic and intimately provable statement. However, this simple concept took over one hundred years and involved more than a dozen mathematicians to finally see it. Throughout the one C that many men pondered this idea, many other problems, solutions, and mathematical concepts were created. I find the Four Coloring Theorem to be very interesting because of its apparent simplicity diametric with its long, 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 find that he only needed four different colors 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 recount him if it was true or not. De Morgan was unsure, so he asked the same question to Hamilton i n Dublin. Hamilton was unable to help, so De Morgan continued to ask other prominent mathematicians. In the US, Charles Peirce move to prove the Four Color Conjecture in the 1860s and continued to for the remainder of his life. In 1879, Cayley wrote a paper to the Royal 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, eleven 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 well-nigh a region is... ...actually quite fun as well. They dont really have a real importance in the real world. The Four Color Theorem isnt personnel casualty to save any lives or make life that much easier. However, it does make map coloring more simple by re quiring only four colors. Bibliography (1) Fritsh, Rudolf and Gerda, The Four-Color Theorem, Springer-Verlag, sensitive 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, celestial latitude 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.