Hypergraph removal
= Hypergraph removal
= Hypergraph removal lemma
{synonym}
For each fixed finite <uniform hypergraph> $F$, having few copies of $F$ forces small edge-edit distance from an $F$-free <hypergraph>. More precisely, for every $\eta>0$ there is $\rho>0$ such that fewer than $\rho v^{|V(F)|}$ copies can be eliminated by deleting fewer than $\eta v^r$ edges in an $r$-uniform <hypergraph>. <Strong regularity for three-uniform hypergraphs> and a relative counting lemma prove the case $r=3$.