Triangle removal lemma
From Polymath Wiki
Triangle removal lemma: If a graph on n vertices contains [math]\displaystyle{ o(n^3) }[/math] triangles, then all triangles can be deleted by removing at most [math]\displaystyle{ o(n^2) }[/math] edges.
This lemma was first proven by Ruzsa and Szemerédi, who observed that it implies Roth's theorem. Solymosi later observed that it also implies the corners theorem.
[Discussion about how one might hope to use the triangle removal lemma for DHJ needed here.]
