Geodesic
Graphs with many copies of a given subgraph
The electronic journal of combinatorics, Tome 15 (2008)
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Let $c>0$, and $H$ be a fixed graph of order $r$. Every graph on $n$ vertices containing at least $cn^{r}$ copies of $H$ contains a "blow-up" of $H$ with $r-1$ vertex classes of size $\big\lfloor c^{r^{2}}\ln n\big\rfloor $ and one vertex class of size greater than $n^{1-c^{r-1}}$. A similar result holds for induced copies of $H$.
DOI : 10.37236/881
Classification : 05C35
Mots-clés : graphs containing copies of subgraphs, blow up of subgraphs, induced copies of subgraphs 
@article{10_37236_881,
     author = {Vladimir Nikiforov},
     title = {Graphs with many copies of a given subgraph},
     journal = {The electronic journal of combinatorics},
     year = {2008},
     volume = {15},
     doi = {10.37236/881},
     zbl = {1158.05323},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/881/}
}
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DO  - 10.37236/881
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%T Graphs with many copies of a given subgraph
%J The electronic journal of combinatorics
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Vladimir Nikiforov. Graphs with many copies of a given subgraph. The electronic journal of combinatorics, Tome 15 (2008). doi: 10.37236/881

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