Date: Mar 6, 2014 11:12 PM
Subject: Re: 4 colors problem

On 3/6/2014 7:37 PM, stumblin' in wrote:
> I am working under the premise that the 4 color theorem works.
> Working with the new unit pattern,
> a b
> c d
> presents its own challenges and peculiarities.
> For instance,
> When the 2nd and 3rd countries unite,
> a b a b a b a b... we could do -->
> a b b a b a b a... swap the rest of the row or we could do -->
> b a a b a b a b...
> If other countries unite on the same row that could require
> another swapping similar to above...
> If countries unite with countries on other rows...
> It changes the whole landscape...
> Whoever said the 4 color theorem was just a tip of an iceberg was right...
> There seems no end in sight...
> Maybe there never will be...

It is the four colors but mostly the three. It is the completions
on the spherical that are five colors but those are not planar. The
build in the four and the three, is in values that as a scale would
work out easier to named ranges and classifications then as to

Maybe if where the planar maps were also adjacent when they shared
vertices besides when they shared borders, then more regions would
be adjacent. For example, a pi chart could have any number of
categories, all sharing a point. In systems and classifications
where it is relevant to figure out how many colors of paint to mix,
or rather indicators in an atomic alphabet then as to color for
interpretation, planar adjacency on the map coloring, and that
compared to a language L* of all the colors other regions of the map
may well or not need that many other colors to have their own (for
example a border around it, here in the planar of the graph). Then,
components together and having so many colors, having a boundary
around them all, adds the color of the boundary, where they are all
adjacent in the middle the boundary is all of them and each has
their own. Then, the four color problem would be a case of that,
that with only edge connections as how the borders work out then
that there are only adjacencies of edges and not vertices alone,
that it is four colors in the planar. Basically the vertex is a
clear region or colorless there.

Seems put more numbers at it on the graph characteristics simply,
they'd simply build more numbers of their graph characteristic.
Probably map to categories, too, probably already does.

Then the point of the academic is finding the right academic that
(for example) has developed then what are for example the values of
these, then for example of natural observations where there are
chiralities, etcetera.

Then, building more regions into the map, that aren't colored, here
could work to partitioning the map, that then in the planar, as
those are closed in circuits, that all the subgraphs would be
connected orthogonally from the borders. Then, any neighbor to the
clear regions would have a two-color proof about them instead of a
three-color proof.