Date: Mar 6, 2014 11:12 PM Author: ross.finlayson@gmail.com 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

interpolation.

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.