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.

Publication Title

Bulletin of the London Mathematical Society