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Combinatorica

, Volume 8, Issue 4, pp 323–332 | Cite as

Some Ramsey-Turán type results for hypergraphs

  • P. Frankl
  • V. Rödl
Article

Abstract

To everyk-graphG letπ(G) be the minimal real numberπ such that for everyε>0 andn>n0(ε,G) everyk-graphH withn vertices and more than (π+ε) (\(\left( {\pi + \varepsilon } \right)\left( {\begin{array}{*{20}c} n \\ k \\ \end{array} } \right)\)) edges contains a copy ofG. The real numberϱ (G) is defined in the same way adding the constraint that all independent sets of vertices inH have sizeo(n). Answering a problem of Erdős and Sós it is shown that there exist infinitely manyk-graphs with 0<ϱ(G)<π(G) for everyk≧3. It is worth noting that we were unable to find a singleG with the above property.

AMS subject classification code (1980)

05 C 55 05 C 65 

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Copyright information

© Akadémiai Kiadó 1988

Authors and Affiliations

  • P. Frankl
    • 1
  • V. Rödl
    • 2
  1. 1.CNRSParisFrance
  2. 2.FJFI, ČVUTPragueCzechoslovakia

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