  In [5] Graham and Rothschild consider a geometric Ramsey problem: finding the
least n such that if all edges of the complete graph on the points {+1,-1}^n
are 2-colored, there exist 4 coplanar points such that the 6 edges between them
are monochromatic. They give an explicit upper bound: F(F(F(F(F(F(F(12))))))),
where F(m) = 2^^(m)^^3, an extremely fast-growing function. By reducing the
problem to a variant of the Hales-Jewett problem, we find an upper bound which
is between F(4) and F(5).
