Regular clique counting lemma
= Regular clique counting lemma
{title2=$\#K_r\ge\delta n^r$}
For fixed $r$ and positive density threshold $\lambda$, sufficiently regular pairwise dense bipartite graphs between $r$ disjoint equal-sized vertex classes contain at least $\delta n^r$ transversal <cliques>, for some $\delta>0$. A greedy embedding maintains common neighbourhoods and discards the small set of vertices with atypical degrees into them. The constants depend only on $r,\lambda$.