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Bulletin of the London Mathematical Society 2008 40(1):23-25; doi:10.1112/blms/bdm093
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© 2008 London Mathematical Society

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

Vladimir Nikiforov

Department of Mathematical Sciences
University of Memphis
Memphis TN 38152
USA

Received 20 March 2007. Revision received 13 July 2007.

Let r≥2 and c>0. Every graph on n vertices with at least cnr cliques on r vertices contains a complete r-partite subgraph with r–1 parts of size {lfloor} crlog n{rfloor} and one part of size greater than n1–cr–1. This result implies a quantitative form of the Erdös–Stone theorem.

2000 Mathematics Subject Classification 05C35 (primary).


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