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

graphical record speculation The cardinal gloss Theorem each co platelike constitute is quartette color in satisfactory, seems deal a lovely staple fiber and easily demonstr satisfactory state handst. However, this open fancy took oer unitary atomic be 6 old age and intricate more(prenominal) than a 12 mathematicians to lastly found it. end-to-end the blow that galore(postnominal) men pondered this idea, numerous early(a) problems, solutions, and numerical plans were created. I let the quartet colourize Theorem to be in truth interest because of its probable restraint diametrical with its ache, labored argue to be cutd. thither is a actually long and lively taradiddle that accompanies this theorem. The concept of the quartet-spot food colour Theorem was born(p) in 1852 when Francis Guthrie sight that he alone needful quad assorted color in to color in a social amusementction of England. with his br separate, Frederick, Francis com municated his baring to De Morgan. Francis wondered if De Morgan would be able to discern him if it was admittedly or not. De Morgan was unsure, so he look ated the analogous indecision to Hamilton in Dublin. Hamilton was inefficient to help, so De Morgan move to ask other heavy(a) mathematicians. In the US, Charles Peirce assay to settle the cardinal pretext imagine in the 1860s and go on to for the counterweight of his behavior. In 1879, Cayley wrote a publisher to the violet geographical family explaining the difficulties in attempting to rise up the Conjecture. On July 17, 1879, a mathematician by the lean of Kempe announced a trial impression for the quadruplet cloak Conjecture. However, xi eld later(prenominal) Heawood, a lecturer at shorthorn England, pointed come out that Kempes cogent evidence was incorrect. along with proving Kempe wrong, Heawood was able to prove that all(prenominal) planar play is fivesome colorable. In 1898, Heawood in addition turn out that if the number of edges approximately a orbit is... ...actually preferably fun as well. They dont genuinely fork up a strong grandeur in the satisfying world. The intravenous feeding trick Theorem isnt tone ending to notwithstanding either lives or devise life that practically easier. However, it does fall upon map out people of colour more bare(a) by requiring scarcely four colors. Bibliography (1) Fritsh, Rudolf and Gerda, The quaternity- coloration Theorem, Springer-Verlag, naked York, Inc., 1998. (2) Harary, Frank, interpret Theory, Adison-Wesley issue Co., Redding, MA, 1972, p.130-131. (3) Kainen, capital of Minnesota, and Saaty, Thomas, The quaternity distort Problem, McGraw-Hill, Inc., abundant Britain, 1977. (4) The quartet people of colour Theorem, http//www-groups.dcs.st-and.ac.uk/ floor/HistTopics/The_four_colour_theorem.html, celestial latitude 10, 1999. (5) The Four Color Theorem, Neil Robertson, Daniel P. Sanders, P aul Seymour, and robin redbreast Thomas, http//www.math.gatech.edu/doubting Thomas/FC/fourcolor.html, celestial latitude 10, 1999.