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I'm currently reading about the four color theorem and while I understand that it's been proven to be true, I don't see specific information about the way of coloring required for it - thus, I began to wonder, is there some specific way of coloring needed for the theorem to hold true or is it guaranteed to always reach the 4-color coloring even if you pick the colors at random?

I mean - if you were given an blank (i.e. non-colored) map and were given a task to color it, is there a wrong way of doing it or is it that if you're playing by the general rules of the problem (i.e. you choose colors so that no two are adjacent) and you decide to go, say, layer-by-layer outwards from the center, you'll always achieve a proper coloring?

If there are specific rules to achieve a guaranteed coloring, what are they?

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The right way is, basically, whichever way works. There are algorithms that have been found since the theorem was proven, however; here is one (behind a paywall). I'll leave it to you whether that's good enough.

As for whether there is a wrong way, yes, there is. Take, for instance, the following map:

enter image description here

If, for instance, you were to start carelessly coloring the four outer regions using one of each color, the middle region cannot be colored.

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    Thanks for the reply. Do you happen to know if there have been any tests about how often the random coloring doesn't work in general, though? I mean, in the great example you provided the mindlesss-greedy approach would surely fail but it looks quite like a corner case - does it fail when speaking about the totality of maps that frequently too? – 2017-02-02
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    @Straightfw That depends entirely on how complicated the map is, but I have no idea about any actual research on the subject. – 2017-02-02
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    I see, thank you. In that case, I have one last question - is there some general consensus about what dictates how complicated the map is? Is it the average number of neighbours of a cell or a discrepancy between the least and most neighbours a cell in the map has or a completely different metric? – 2017-02-02
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    @Straightfw I honestly have no idea. I don't know much more about the 4CT than what I've written here to be honest. – 2017-02-02
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    Got it, thanks for the help anyway :) – 2017-02-02