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In Graham and Rothschild (1971), 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}N∗ are 2-colored, there exist 4 coplanar points such that the 6 edges between them are monochromatic. They give an explicit upper bound: N∗≤F(F(F(F(F(F(F(12,3),3),3),3),3),3),3), where F(m,n)=2↑mn, an extremely fast-growing...
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