On Wednesday, March 5, 2014 3:11:19 PM UTC-6, swtch...@gmail.com wrote: > Partial coloring using a specific sequence of given 4 colors, followed by another specific (but different from the previous) sequence of given 4 colors (to be used for the next row of countries), known as a unit pattern, can follow simple rules to color the whole map (of the countries shaped as squares of equal size) guaranteeing that no matter how large the map gets (to infinity in all four directions), there will be no two countries sharing the same color, thus proving that the theorem is valid.
You don't even know what the theorem says, as the paragraph above shows.
The theorem states: GIVEN a planar map, in which countries are connected, it is possible to produce a *FULL* coloring using no more than four colors in which no two countries that share a border (which is more than isolated points) are assigned the same color.
It does not deal with "partial colorings".
> Convention says common points don't count, only borderlines count, but here common points count the same as borderlines.
Then you are not talking about the Four Color Map theorem. You are talking about something else.
And if you are talking about this something else, then what you are doing is completely useless and irrelevant, since a pie chart with n "slices" provides you with a map that requires at least n colors, for any positive integer n and all your ruminations are useless and irrelevant.
Clear now, or will you again ignore it and repeat the same ignorant nosense in the hope that repetition will stand in for information?