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C00002 00002	A map is a finite set of vertices + a set of unordered pairs of these vertices.
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A map is a finite set of vertices + a set of unordered pairs of these vertices.
A partial coloring is a partial function from the vertices to colors
satisfying the condition that paired countries are colored differently.
A Kempe component of a pair of colors is a maximal subset of the vertices connected
in the pair of colors in the partial map.  kempe(subset, partial map).
Finiteness and maximality should get general axiomatizations so that
they can be used freely in the specific axiomatization.

Many specifically computational concepts like a chain of reductions of
a graph should be explicitly defined.

We need to be able to describe the coloring "algorithm" in terms like

	Remove the countries with ≤4 neighbors from the graph continuing until
no more can be removed.

	Color the reduced graph exhausively.  A simpler algorithm fails if the
reduced graph is non-empty.

	Color the remaining countries in reverse order to their removal, using
Kempe transformations where necessary.

The steps should be described precisely but the order of
removing countries should be left undefined as this corresponds to
our informal idea of the algorithm.