$C_5$ is almost a fractalizer
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arXiv
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866912903636975616 |
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| author | Lidický, Bernard Mattes, Connor Pfender, Florian |
| author_facet | Lidický, Bernard Mattes, Connor Pfender, Florian |
| contents | We determine the maximum number of induced copies of a 5-cycle in a graph on $n$ vertices for every $n$. Every extremal construction is a balanced iterated blow-up of the 5-cycle with the possible exception of the smallest level where for $n=8$, the Möbius ladder achieves the same number of induced 5-cycles as the blow-up of a 5-cycle on 8 vertices.
This result completes work of Balogh, Hu, Lidický, and Pfender [Eur. J. Comb. 52 (2016)] who proved an asymptotic version of the result. Similarly to their result, we also use the flag algebra method but we extend its use to small graphs. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2102_06773 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | $C_5$ is almost a fractalizer Lidický, Bernard Mattes, Connor Pfender, Florian Combinatorics We determine the maximum number of induced copies of a 5-cycle in a graph on $n$ vertices for every $n$. Every extremal construction is a balanced iterated blow-up of the 5-cycle with the possible exception of the smallest level where for $n=8$, the Möbius ladder achieves the same number of induced 5-cycles as the blow-up of a 5-cycle on 8 vertices. This result completes work of Balogh, Hu, Lidický, and Pfender [Eur. J. Comb. 52 (2016)] who proved an asymptotic version of the result. Similarly to their result, we also use the flag algebra method but we extend its use to small graphs. |
| title | $C_5$ is almost a fractalizer |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2102.06773 |