# Maximizing five-cycles in Kr-free graphs

@article{Lidick2020MaximizingFI, title={Maximizing five-cycles in Kr-free graphs}, author={B. Lidick{\'y} and K. Murphy}, journal={arXiv: Combinatorics}, year={2020} }

The Erdos Pentagon problem asks to find an n-vertex triangle-free graph that is maximizing the number of 5-cycles. The problem was solved using flag algebras by Grzesik and independently by Hatami, Hladky, Kral, Norin, and Razborov. Recently, Palmer suggested the general problem of maximizing the number of 5-cycles in K_{k+1}-free graphs. Using flag algebras, we show that every K_{k+1}-free graph of order n contains at most \[\frac{1}{10k^4}(k^4 - 5k^3 + 10k^2 - 10k + 4)n^5 + o(n^5)\] copies of… Expand

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#### References

SHOWING 1-10 OF 41 REFERENCES

Minimizing the number of 5-cycles in graphs with given edge-density

- Mathematics, Computer Science
- Combinatorics, Probability and Computing
- 2019

The minimum size of 3-graphs without a 4-set spanning no or exactly three edges

- Computer Science, Mathematics
- Eur. J. Comb.
- 2011

On the maximal number of certain subgraphs inKr-free graphs

- Mathematics, Computer Science
- Graphs Comb.
- 1991

Applications of the Semi-Definite Method to the Turán Density Problem for 3-Graphs

- Computer Science, Mathematics
- Combinatorics, Probability and Computing
- 2012

On the number of pentagons in triangle-free graphs

- Computer Science, Mathematics
- J. Comb. Theory, Ser. A
- 2013

Counting copies of a fixed subgraph in F-free graphs

- Mathematics, Computer Science
- Eur. J. Comb.
- 2019

Many T copies in H-free graphs

- Mathematics, Computer Science
- Electron. Notes Discret. Math.
- 2015