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

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

2007-03-19

arxiv.org/abs/math/0703554v3

Mathematics

Combinatorics

Some polishing. Updated references

Scientific paper

We prove that for all $r\geq2$ 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 $\lfloor c^{r}\log n \rfloor.$ This result implies a concise form of the
Erd\H{o}s-Stone theorem.

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