Local maximum of inducibility profiles
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866916013234192384 |
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| author | Balogh, József Lidický, Bernard |
| author_facet | Balogh, József Lidický, Bernard |
| contents | For a graph $G$ and $e\in [0,1]$, denote by $I_G(e)$ the supremum of densities of $G$ over $n$-vertex graphs with edge density $e$ as $n$ goes to infinity. Liu, Mubayi and Reiher asked if there exists a graph $G$, where $I_G(e)$ has a non-trivial local maximum. In this note we resolve their problem by showing that $I_{K_{2,2,1}}(e)$ has at least two local maxima in $(0,1)$. Additionally, we determine $I_{K_{2,2,1}}(e)$, when $e=(k-1)/k$ for every integer $k\ge 3.$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_15021 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Local maximum of inducibility profiles Balogh, József Lidický, Bernard Combinatorics For a graph $G$ and $e\in [0,1]$, denote by $I_G(e)$ the supremum of densities of $G$ over $n$-vertex graphs with edge density $e$ as $n$ goes to infinity. Liu, Mubayi and Reiher asked if there exists a graph $G$, where $I_G(e)$ has a non-trivial local maximum. In this note we resolve their problem by showing that $I_{K_{2,2,1}}(e)$ has at least two local maxima in $(0,1)$. Additionally, we determine $I_{K_{2,2,1}}(e)$, when $e=(k-1)/k$ for every integer $k\ge 3.$ |
| title | Local maximum of inducibility profiles |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2605.15021 |