A problem of Erdős and Sós on 3-graphs
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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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