Re: Why Archimedes Plutonium will never proof the 4CT


Proginoskes wrote:
> [...]
> Here are the two basic facts that AP is ignoring:
> [...]
>
> (2) If the 4CT is false, that does not immediately imply that there are
> 5 countries which are adjacent to each other. [...]

And now I will give another example. This example has 12 countries, and
they will be called A, B, C, .., L. The following pairs of countries
share a boundary:

A and B, B and C, C and D, D and E, E and A
A and G, G and C, C and I, I and E, E and F, F and B, B and H, H and D,

D and J, J and A
F and K, G and K, H and K, I and K, J and K
L with every other country.

Now if you have a map with these "adjacencies", it will require at
least 5 colors:

(a) If you just color A, B, C, D, and E, you will need at least 3
colors.
(b) If you just color A through K, you will need at least 4 colors.
(c) L has to receive a different color than ANY other country.

So the whole map requires 5 colors (at least). Furthermore, you cannot
find 5 countries which are all adjacent to each other. In fact, you
can't even find FOUR countries which are all adjacent to each other.

--- Christopher Heckman

.

Relevant Pages
Quantcast