# A problem of Erdős and Sós on 3-graphs

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DOI: 10.1007/s11856-015-1267-4

- Cite this article as:
- Glebov, R., Král’, D. & Volec, J. Isr. J. Math. (2016) 211: 349. doi:10.1007/s11856-015-1267-4

- 4 Citations
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## Abstract

We show that for every *ɛ* > 0 there exist *δ* > 0 and *n*_{0} ∈ ℕ such that every 3-uniform hypergraph on *n* ≥ *n*_{0} vertices with the property that every *k*-vertex subset, where *k* ≥ *δn*, induces at least \(\left( {\frac{1}
{2} + \varepsilon } \right)\left( {\begin{array}{*{20}c}
k \\
3 \\
\end{array} } \right)\) edges, contains *K*_{4}^{−} as a subgraph, where *K*_{4}^{−} is the 3-uniform hypergraph on 4 vertices with 3 edges. This question was originally raised by Erdős and Sós. The constant 1/4 is the best possible.

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© Hebrew University of Jerusalem 2016