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Disperse hypergraphs
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DOI：10.1017/S0963548325100205.png)
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Abstract
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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 $n<^>{\Omega _{\ell }(1)}$ , answering a question of the first author and Tomon. To this end, we prove several structural properties of disperse hypergraphs.
Keywords:
Erdos-Hajnal conjecture
Homogeneous sets in hypergraphs
Journal
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0.8
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30
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