A problem of Erdős and Sós on 3-graphs

Conference paper
Part of the CRM Series book series (PSNS, volume 16)


We show that for every ε > 0 there exist δ > 0 and n 0 ∈ N such that every 3-uniform hypergraph on nn 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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© Scuola Normale Superiore Pisa 2013

Authors and Affiliations

  1. 1.Mathematics Institute and DIMAPUniversity of WarwickCoventryUK
  2. 2.Mathematics Institute, DIMAP and Department of Computer ScienceUniversity of WarwickCoventryUK

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