well i know this has been a perennially interesting question eric
but how about first showing us a theoretical example of a topology
requiring a 5th color
& then at least we will know what to seek on your behalf in reality
otherwise i think we may only continue to peck away at this huge
offering
& finally shrug our shoulders
even if we had the geographical knowledge to apply to it
--- 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?
>
> 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