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arXiv · 1608.03241

An Erdős-Gallai type theorem for uniform hypergraphs

Akbar Davoodi·Ervin Győri·Abhishek Methuku·Casey Tompkins
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Abstract

A well-known theorem of Erdős and Gallai asserts that a graph with no path of length $k$ contains at most $\frac{1}{2}(k-1)n$ edges. Recently Győri, Katona and Lemons gave an extension of this result to hypergraphs by determining the maximum number of hyperedges in an $r$-uniform hypergraph containing no Berge path of length $k$ for all values of $r$ and $k$ except for $k=r+1$. We settle the remaining case by proving that an $r$-uniform hypergraph with more than $n$ hyperedges must contain a Berge path of length $r+1$.

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Akbar Davoodi, Ervin Győri, Abhishek Methuku, Casey Tompkins. 2017-11-18. An Erdős-Gallai type theorem for uniform hypergraphs. https://doi.org/10.1016/j.ejc.2017.10.006

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