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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2311.17573 |
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| _version_ | 1866929391528837120 |
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| author | Zhou, Junpeng Yuan, Xiying Wang, Wen-Huan |
| author_facet | Zhou, Junpeng Yuan, Xiying Wang, Wen-Huan |
| contents | An $r$-uniform hypergraph ($r$-graph) is linear if any two edges intersect at most one vertex. For a graph $F$, a hypergraph $H$ is Berge-$F$ if there is a bijection $ϕ:E(F)\rightarrow E(H)$ such that $e\subseteq ϕ(e)$ for all $e$ in $E(F)$. In this paper, a kind of stability result for Berge-$K_{3,t}$ linear $r$-graphs is established. Based on this stability result, an upper bound for the linear Turán number of Berge-$K_{3,t}$ is determined. For an $r$-graph $H$, let $\mathcal{A}(H)$ be the adjacency tensor of $H$. The spectral radius of $H$ is the spectral radius of the tensor $\mathcal{A}(H)$. Some bounds for the maximum spectral radius of connected Berge-$K_{3,t}$-free linear $r$-graphs are obtained. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_17573 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A stability result for Berge-$K_{3,t}$ $r$-graphs and its applications Zhou, Junpeng Yuan, Xiying Wang, Wen-Huan Combinatorics An $r$-uniform hypergraph ($r$-graph) is linear if any two edges intersect at most one vertex. For a graph $F$, a hypergraph $H$ is Berge-$F$ if there is a bijection $ϕ:E(F)\rightarrow E(H)$ such that $e\subseteq ϕ(e)$ for all $e$ in $E(F)$. In this paper, a kind of stability result for Berge-$K_{3,t}$ linear $r$-graphs is established. Based on this stability result, an upper bound for the linear Turán number of Berge-$K_{3,t}$ is determined. For an $r$-graph $H$, let $\mathcal{A}(H)$ be the adjacency tensor of $H$. The spectral radius of $H$ is the spectral radius of the tensor $\mathcal{A}(H)$. Some bounds for the maximum spectral radius of connected Berge-$K_{3,t}$-free linear $r$-graphs are obtained. |
| title | A stability result for Berge-$K_{3,t}$ $r$-graphs and its applications |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2311.17573 |