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The Four Color Theorem

By Yuriy Brun


Abstract. In this paper, we introduce graph theory, and discuss the Four Color Theorem. Then we prove several theorems, including Euler’s formula and the Five Color Theorem. 1. Introduction. According to [1, p. 19], the Four Color Theorem has fascinated people for almost a century and a half. It dates back to 1852 when Francis Guthrie, while trying to color the map of counties of England, noticed that four colors suffice. He asked his brother Frederick if any map can be colored using four colors so that different colors appear on adjacent regions — that is, regions sharing a common boundary segment

Year: 2011
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