The Earth-Moon problem is a special case of the empire problem for countries with 
disjoint regions, with one region of each country lying
on the Earth and one on the Moon (Ringel 1959; Frederickson 2002, p. 32). The
additional constraint means that fewer than 12 colors might suffice. And in fact,
Ringel (1959) gave an example requiring only 8 colors. Gardner (1980) reported an
example requiring 9 colors, but it is not known if configurations exist requiring
10, 11, or 12 colors (Frederickson 2002, p. 32).
Earth-Moon Problem
See also
Empire Problem, Four-Color TheoremExplore with Wolfram|Alpha
References
Frederickson, G. N. Hinged Dissections: Swinging & Twisting. New York: Cambridge University Press, 2002.Gardner, M. "Mathematical Recreations: The Coloring of Unusual Maps Leads Into Uncharted Territory." Sci. Amer. 242, 14-22, Feb. 1980.Ringel, G. Färbungsprobleme auf Flachen und Graphen. Berlin: Deutsche Verlag der Wissenschaften, 1959.Referenced on Wolfram|Alpha
Earth-Moon ProblemCite this as:
Weisstein, Eric W. "Earth-Moon Problem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Earth-MoonProblem.html