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arXiv · 2508.09841

The Brown-Erdős-Sós conjecture in dense triple systems

Giovanne Santos·Mykhaylo Tyomkyn
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Abstract

The famous Brown-Erdős-Sós conjecture from 1973 states, in an equivalent form, that for any fixed $δ>0$ and integer $k\geq 3$ every sufficiently large linear $3$-uniform hypergraph of size $δn^2$ contains some $k$ edges spanning at most $k+3$ vertices. We prove it to hold for $δ>4/5$, establishing the first bound of this kind.

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Giovanne Santos, Mykhaylo Tyomkyn. 2025-08-13. The Brown-Erdős-Sós conjecture in dense triple systems. https://arxiv.org/abs/2508.09841

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