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\require{AMSmath}
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Graphs and Graph Theory
In the branch of mathematics called Graph Theory, a graph bears no relation to the graphs that chart data, such as the progress of the stock market or the growing population of the planet. Graph paper is not particularly useful for drawing the graphs of Graph Theory.
The Four Color Theorem
How many different colors are sufficient to color the countries on a map in such a way that no two adjacent countries have the same color? After examining a wide variety of different planar graphs, one discovers the apparent fact that every graph, regardless of size or complexity, can be colored with just four distinct colors.
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