The Four-Color Theorem (Topological Version)

Abstract

Generally, when one talks about four specific colors, then one frequently chooses the colors blue, yellow, green, and red.¹ For the most part, we will designate these four colors by the numbers 1, 2, 3, 4, and sometimes also by 0,1, 2, 3. This has an additional advantage. One can then extend the discussion to more than four colors without any further difficulty. In fact, one is able to color with n colors, where n is any natural number (n ∈ ℕ). If $\mathcal{L}$ is a map, we denote by ${\mathcal{M}_\mathcal{L}}$ the set of all countries of $\mathcal{L}$. By “coloring” of a map, we intuitively mean that we have one color corresponding to each country of the map (see page 44).