Gardado en:
| Main Authors: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Subjects: | |
| Acceso en liña: | https://arxiv.org/abs/2605.15021 |
| Tags: |
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Table of 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 $k\ge 3.$