Graphs with many r-cliques have large complete r-partite subgraphs
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 ⌊ crlog n⌋ and one part of size greater than n1-c r-1. This result implies a quantitative form of the Erdös-Stone theorem. © 2008 London Mathematical Society.
Bulletin of the London Mathematical Society
Nikiforov, V. (2008). Graphs with many r-cliques have large complete r-partite subgraphs. Bulletin of the London Mathematical Society, 40 (1), 23-25. https://doi.org/10.1112/blms/bdm093