On Tuesday, March 4, 2014 7:24:11 PM UTC+1, swtch...@gmail.com wrote: > ABABABA > BABABAB > ABABABA > > This checkered coloring scheme would not work since same colors are used in the adjacent countries in this case.
Why ? No "A" is adjacent to another "A" and no "B" is adjacent to another "B".
Remember that in map coloring two regions are not considered adjacent if they share just a corner, as in the scheme above.
As reported in Wikipedia (under Four colors th.):
"In mathematics, the four color theorem, or the four color map theorem, states that, given any separation of a plane into contiguous regions, producing a figure called a map, no more than four colors are required to color the regions of the map so that no two adjacent regions have the same color.
Two regions are called ADJACENT if they share a COMMON BOUNDARY that is NOT a CORNER, where corners are the points shared by three or more regions.
For example, in the map of the United States of America, Utah and Arizona are adjacent, but Utah and New Mexico, which only share a point that also belongs to Arizona and Colorado, are not."