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arXiv · 2404.00873

Localized Version of Hypergraph Erdos-Gallai Theorem

Kai Zhao·Xiao-Dong Zhang
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Abstract

This paper focuses on extensions of the classic Erd\H{o}s-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 Erd\H{o}s-Gallai Theorem.

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Kai Zhao, Xiao-Dong Zhang. 2024-04-01. Localized Version of Hypergraph Erdos-Gallai Theorem. https://arxiv.org/abs/2404.00873

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