English

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

Combinatorics 2014-02-26 v3

Abstract

We prove that for all r2r\geq2 and c>0, every graph of order n with at least cn^{r} cliques of order r contains a complete r-partite graph with each part of size crlogn.\lfloor c^{r}\log n \rfloor. This result implies a concise form of the Erd\H{o}s-Stone theorem.

Keywords

Cite

@article{arxiv.math/0703554,
  title  = {Graphs with many r-cliques have large complete r-partite subgraphs},
  author = {Vladimir Nikiforov},
  journal= {arXiv preprint arXiv:math/0703554},
  year   = {2014}
}

Comments

Some polishing. Updated references

R2 v1 2026-07-22T17:52:53.533Z