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A problem of Erdos and Sos on 3-graphs

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We show that for every positive epsilon there exist positive delta and n_0 such that every 3-uniform hypergraph on n>=n_0 vertices with the property that every k-vertex subset, where k>=deltan, induces at least (1/4 + epsilon){k \choose 3} edges, contains K4- as a subgraph, where K4- is the 3-uniform hypergraph on 4 vertices with 3 edges. This question was originally raised by Erdos and Sos. The constant 1/4 is the best possible. Joint work with Dan Kral and Jan Volec.

This talk is part of the Combinatorics Seminar series.

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