Spectral bipartite Turan problems on linear hypergraphs
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866908456238186496 |
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| author | She, Chuan-Ming Fan, Yi-Zheng Kang, Liying |
| author_facet | She, Chuan-Ming Fan, Yi-Zheng Kang, Liying |
| contents | Let $F$ be a graph, and let $\mathcal{B}_r(F)$ be the class of $r$-uniform Berge-$F$ hypergraphs. In this paper, we establish a relationship between the spectral radius of the adjacency tensor of a uniform hypergraph and its local structure through walks. Based on the relationship, we give a spectral asymptotic bound for $\mathcal{B}_{r}(C_3)$-free linear $r$-uniform hypergraphs and upper bounds for the spectral radii of $\mathcal{B}_{r}(K_{2,t})$-free or $\{\mathcal{B}_{r}(K_{s,t}),\mathcal{B}_{r}(C_{3})\}$-free linear $r$-uniform hypergraphs, where $C_{3}$ and $K_{s,t}$ are respectively the triangle and the complete bipartite graph with one part having $s$ vertices and the other part having $t$ vertices. Our work implies an upper bound for the number of edges of $\{\mathcal{B}_{r}(K_{s,t}),\mathcal{B}_{r}(C_{3})\}$-free linear $r$-uniform hypergraphs and extends some of the existing research on (spectral) extremal problems of hypergraphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_02064 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Spectral bipartite Turan problems on linear hypergraphs She, Chuan-Ming Fan, Yi-Zheng Kang, Liying Combinatorics 05C35, 05C65 Let $F$ be a graph, and let $\mathcal{B}_r(F)$ be the class of $r$-uniform Berge-$F$ hypergraphs. In this paper, we establish a relationship between the spectral radius of the adjacency tensor of a uniform hypergraph and its local structure through walks. Based on the relationship, we give a spectral asymptotic bound for $\mathcal{B}_{r}(C_3)$-free linear $r$-uniform hypergraphs and upper bounds for the spectral radii of $\mathcal{B}_{r}(K_{2,t})$-free or $\{\mathcal{B}_{r}(K_{s,t}),\mathcal{B}_{r}(C_{3})\}$-free linear $r$-uniform hypergraphs, where $C_{3}$ and $K_{s,t}$ are respectively the triangle and the complete bipartite graph with one part having $s$ vertices and the other part having $t$ vertices. Our work implies an upper bound for the number of edges of $\{\mathcal{B}_{r}(K_{s,t}),\mathcal{B}_{r}(C_{3})\}$-free linear $r$-uniform hypergraphs and extends some of the existing research on (spectral) extremal problems of hypergraphs. |
| title | Spectral bipartite Turan problems on linear hypergraphs |
| topic | Combinatorics 05C35, 05C65 |
| url | https://arxiv.org/abs/2403.02064 |