Extremal problems, partition theorems, symmetric hypergraphs

Abstract

We compare extremal theorems such as Turán’s theorem with their corresponding partition theorems such as Ramsey’s theorem. We derive a general inequality involving chromatic number and independence number of symmetric hypergraphs. We give applications to Ramsey numbers and to van der Waerden numbers.

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References

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    L. Lovász, On the ratio of optimal integral and fractional covers,Discrete Math. 13 (1975), 383–390.

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Spencer, J. Extremal problems, partition theorems, symmetric hypergraphs. Combinatorica 1, 303–307 (1981). https://doi.org/10.1007/BF02579336

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AMS subject classification (1980)

  • 05 C 65
  • 60 C 05
  • 05 C 35