--- In
BoundaryPoint@yahoogroups.com, "Eric Choate" <choatune@y...>
wrote:
> The presence of the Azerbaijani exclave (and many others) means
that
> the present set of national boundaries on earth does not satisfy
the
> prerequesites to apply the Four Color Theorem. Nevertheless, a
four
> color map of the Caucasus can still be made. It's just that it's
> possible to draw borders with exclaves that do make it impossible
to
> color countries with only four colors.
>
> But there are national exclaves that I am unaware of. Most would
be
> small enough that they would be omitted on a world map that is of a
> size that I could find. Does anyone know of an exclave that if it
> were included would force more than four colors?
ok well now that you have thankfully caused such a riot eric
it is good to return to your actual leading question
as well as the follow ons
the united arab emirates if you can ever find the elusive definitive
map of them
& i think also liechtenstein & switzerland
do appear to meet the conditions of the above & below questions in
their primary subdivisions
& if you do allow that any depiction at all of clavity on a map
forces you to color each political entity distinctly
then of course even united states counties will qualify
but it was fun to watch this entire 4color map question get blown
into a whole new question in our bp funhouse mirror
& especially to have found that if we could rationalize the question
enough then there must be real world answers to it
contrary to my earlier assessment
>
> Similarly, I'm not that familiar with the
> states/provinces/cantons/oblasts/etc., of every country. is there
a
> country that cannot produce a four-color map of its political
> subdivisions?
>
> What about US states with counties? Or I'm sure with all the
> gerrymandering in state legislatures, a congressional district map
> somewhere needs a fifth color. Anyone know of one?
>
> eric