Israel Journal of Mathematics

, Volume 211, Issue 1, pp 349–366 | Cite as

A problem of Erdős and Sós on 3-graphs



We show that for every ɛ > 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 kδn, induces at least \(\left( {\frac{1} {2} + \varepsilon } \right)\left( {\begin{array}{*{20}c} k \\ 3 \\ \end{array} } \right)\) 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.


Convergent Sequence Edge Density Dense Graph Extremal Graph Subgraph Frequency 


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© Hebrew University of Jerusalem 2016

Authors and Affiliations

  1. 1.Department of MathematicsETHZurichSwitzerland
  2. 2.Mathematics InstituteDIMAP and Department of Computer Science University of WarwickCoventryUK

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