A problem of Erdős and Sós on 3-graphs

• DOI: 10.1007/s11856-015-1267-4
• Publication Date: 2015-11-28T05:13:49Z
• Authors: Roman Glebov; Daniel Král’; Jan Volec
• Keywords: FOS: Mathematics; Mathematics - Combinatorics; Combinatorics (math.CO); 0102 computer and information sciences; QA; 01 natural sciences

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.