A Note on Induced Ramsey Numbers

  • David Conlon
  • Domingos Dellamonica
  • Steven La Fleur
  • Vojtěch RödlEmail author
  • Mathias Schacht


The induced Ramsey number r ind(F) of a k-uniform hypergraph F is the smallest natural number n for which there exists a k-uniform hypergraph G on n vertices such that every two-coloring of the edges of G contains an induced monochromatic copy of F. We study this function, showing that r ind(F) is bounded above by a reasonable power of r(F). In particular, our result implies that \(r_{\mathrm{ind}}(F) \leq 2^{2^{ct}}\) for any 3-uniform hypergraph F with t vertices, mirroring the best known bound for the usual Ramsey number. The proof relies on an application of the hypergraph container method.


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© Springer International publishing AG 2017

Authors and Affiliations

  • David Conlon
    • 1
  • Domingos Dellamonica
    • 2
  • Steven La Fleur
    • 2
  • Vojtěch Rödl
    • 2
    Email author
  • Mathias Schacht
    • 3
  1. 1.Mathematical InstituteUniversity of OxfordOxfordUK
  2. 2.Department of Mathematics and Computer ScienceEmory UniversityAtlantaUSA
  3. 3.Fachbereich MathematikUniversität HamburgHamburgGermany

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