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>=delta*n, 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.
CITATION STYLE
Glebov, R., Král’, D., & Volec, J. (2013). A problem of Erdős and Sós on 3-graphs. In The Seventh European Conference on Combinatorics, Graph Theory and Applications (pp. 3–8). Scuola Normale Superiore. https://doi.org/10.1007/978-88-7642-475-5_1
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