It appears that there could also be a 3 color theorem, which, if there was, it would be a theorem that states that 3 colors is enough to color a map of any number of countries provided that all the countries are located on the same row with no other rows, either above or below, are present.
The unit pattern for 3 color theorem would be,
a b c
then there can be no other rows because
a b c c b a
wouldn't work, nor any other combination one could try.
So the only way 3 colors can color infinite number of countries without coloring two adjacent countries with same color, would be: