The Four Color Theorem states that any planar graph can be colored using no more than four colors in such a way that no two adjacent regions share the same color. This theorem is closely linked to the properties of planar graphs and Euler's formula, which provides a foundational understanding of the structure of such graphs, as well as to vertex coloring and chromatic numbers that help define how many colors are needed for proper coloring. In map coloring, this theorem provides a practical application for ensuring that adjacent regions can be easily distinguished from each other.
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