This work is based on one of the most famous problem in mathematics: four color theorem. In the introduction, history and examples of the applications of the four color theorem have been examined. Beside the big history of it, four color theorem has a huge application area e.g. in coloring questions, mobile phones, computer science, scheduling activities, security camera placement, wireless communication networks etc. In this work, an application of four color theorem in a specific area has been examined: location area planning. Therefore this essay tries to answer this following question: ‘What are the applications of four color theorem in location area planning?’
Four color theorem is first proposed on October 23, 1852 by Francis Guthrie.
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Another name of the problem is Guthrie’s problem after Francis Guthrie, who first realized the theorem in 1852. Francis Guthrie was trying to color the map of countries of England and then he noticed that four colors sufficed. He asked his brother Frederick whether it was true that needed at least four colors to color a map of the counties of England. All of these methods was used by other mathematicians to make progress on the four-color problem. There are six and five color theorems in mathematics and they have official proves. But to reduce the number of colors from five to four is very difficult. This problem was finally proved by Appel and Haken (1977), they constructed a computer-assisted proof that four colors were sufficient. However some mathematicians do not accept it because it includes comprehensive analysis by computer that cannot done by hand. But the proof is still valid because no errors found yet.
Today, mathematicians are still looking for a new, computer-free solution for four color theorem, and graph theory is one of the main methods used in these studies. I prepared for Math Olympiads in last 5 years, and one of the topics I exposed while studying was graph theory. I have an interest to this problem therefore I decided to write my extended essay about four color theorem. There is an approach to the solution of the four color theorem with graph theory in this