Graham-Rothschild theorem
From Polymath Wiki
Graham-Rothschild theorem (k=3): If all the combinatorial lines in [math]\displaystyle{ [3]^n }[/math] is partitioned into c color classes, and n is sufficiently large depending on c, m, then there is an m-dimensional combinatorial subspace of [math]\displaystyle{ [3]^n }[/math] such that all the combinatorial lines in this subspace have the same color.
This theorem implies the Hales-Jewett theorem.
