Constructions in Ramsey theory

  title={Constructions in Ramsey theory},
  author={Dhruv Mubayi and Andrew Suk},
  journal={Journal of the London Mathematical Society},
  • D. Mubayi, Andrew Suk
  • Published 22 November 2015
  • Mathematics
  • Journal of the London Mathematical Society
We provide several constructions for problems in Ramsey theory. First, we prove a superexponential lower bound for the classical 4‐uniform Ramsey number r4(5,n) , and the same for the iterated (k−4) ‐fold logarithm of the k ‐uniform version rk(k+1,n) . This is the first improvement of the original exponential lower bound for r4(5,n) implicit in work of Erdős and Hajnal from 1972 and also improves the current best known bounds for larger k due to the authors. Second, we prove an upper bound for… 
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