Tetrahedron removal lemma
= Tetrahedron removal lemma
For every $\eta>0$, some $\rho>0$ has this property: a three-<uniform hypergraph> on $v$ vertices with fewer than $\rho v^4$ copies of the <three-uniform tetrahedron> can be made tetrahedron-free by removing fewer than $\eta v^3$ hyperedges. The <four-term progression hypergraph encoding> converts this into the length-four case of the <Szemerédi theorem>.