Israel Journal of Mathematics

, Volume 211, Issue 1, pp 349–366

A problem of Erdős and Sós on 3-graphs


DOI: 10.1007/s11856-015-1267-4

Cite this article as:
Glebov, R., Král’, D. & Volec, J. Isr. J. Math. (2016) 211: 349. doi:10.1007/s11856-015-1267-4


We show that for every ɛ > 0 there exist δ > 0 and n0 ∈ ℕ such that every 3-uniform hypergraph on nn0 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 K4 as a subgraph, where K4 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.

Copyright information

© 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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