Regularity lemmas for hypergraphs and quasi‐randomness

We give a simple proof for Szemerédi's Regularity Lemma and its generalization for k ‐uniform hypergraphs. For fixed k , there are altogether k ‐1 different versions of the regularity lemma for k ‐uniform hypergraphs. The connection between regularity lemmas for hypergraphs and quasi‐random classes of hypergraphs is also investigated.