Graphs with many r -cliques have large complete r -partite subgraphs
Bulletin of the London Mathematical Society
, Volume 40 (1) – Feb 1, 2008
Abstract
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− c r −1 . This result implies a quantitative form of the Erdös–Stone theorem.
