Graphs with many r-cliques have large complete r-partite subgraphs

@inproceedings{Nikiforov2008GraphsWM,
  title={Graphs with many r-cliques have large complete r-partite subgraphs},
  author={Vladimir Nikiforov},
  year={2008}
}
Let r≥2 and c>0. Every graph on n vertices with at least cn r cliques on r vertices contains a complete r-partite subgraph with r−1 parts of size ⌊ c r log n⌋ and one part of size greater than n 1−cr−1 . This result implies a quantitative form of the Erdos-Stone theorem.