Localized Version of Hypergraph Erdos-Gallai Theorem
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929299067502592 |
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| author | Zhao, Kai Zhang, Xiao-Dong |
| author_facet | Zhao, Kai Zhang, Xiao-Dong |
| contents | This paper focuses on extensions of the classic Erdős-Gallai Theorem for the set of weighted function of each edge in a graph. The weighted function of an edge $e$ of an $n$-vertex uniform hypergraph $\mathcal{H}$ is defined to a special function with respect to the number of edges of the longest Berge path containing $e$. We prove that the summation of the weighted function of all edges is at most $n$ for an $n$-vertex uniform hypergraph $\mathcal{H}$ and characterize all extremal hypergraphs that attain the value, which strengthens and extends the hypergraph version of the classic Erdős-Gallai Theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_00873 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Localized Version of Hypergraph Erdos-Gallai Theorem Zhao, Kai Zhang, Xiao-Dong Combinatorics 05C65, 05C35 This paper focuses on extensions of the classic Erdős-Gallai Theorem for the set of weighted function of each edge in a graph. The weighted function of an edge $e$ of an $n$-vertex uniform hypergraph $\mathcal{H}$ is defined to a special function with respect to the number of edges of the longest Berge path containing $e$. We prove that the summation of the weighted function of all edges is at most $n$ for an $n$-vertex uniform hypergraph $\mathcal{H}$ and characterize all extremal hypergraphs that attain the value, which strengthens and extends the hypergraph version of the classic Erdős-Gallai Theorem. |
| title | Localized Version of Hypergraph Erdos-Gallai Theorem |
| topic | Combinatorics 05C65, 05C35 |
| url | https://arxiv.org/abs/2404.00873 |