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arXiv · 2503.21052

Disperse Hypergraphs

Lior Gishboliner·Ethan Honest
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Abstract

For $\ell \geq 3$, an $\ell$-uniform hypergraph is disperse if the number of edges induced by any set of $\ell+1$ vertices is 0, 1, $\ell$ or $\ell+1$. We show that every disperse $\ell$-uniform hypergraph on $n$ vertices contains a clique or independent set of size $n^{Ω_{\ell}(1)}$, answering a question of the first author and Tomon. To this end, we prove several structural properties of disperse hypergraphs.

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Lior Gishboliner, Ethan Honest. 2025-08-23. Disperse Hypergraphs. https://arxiv.org/abs/2503.21052

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