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On Generalized Ramsey Numbers for 3-Uniform Hypergraphs


  • Contract grant sponsor: NSF; contract grant number: DMS-0969092.


The well-known Ramsey number math formula is the smallest integer n such that every math formula-free graph of order n contains an independent set of size u. In other words, it contains a subset of u vertices with no K2. Erdős and Rogers introduced a more general problem replacing K2 by math formula for math formula. Extending the problem of determining Ramsey numbers they defined the numbers

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where the minimum is taken over all math formula-free graphs G of order n. In this note, we study an analogous function math formula for 3-uniform hypergraphs. In particular, we show that there are constants c1 and c2 depending only on s such that

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