# A problem of Erdős and Sós on 3-graphs

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## Abstract

We show that for every ε > 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 (1/4 + ɛ) 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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