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REFINEMENT OF HOMOGENEITY AND RAMSEY NUMBERS

  • Kim, Hwajeong (Department of Mathematics Hannam University) ;
  • Lee, Gyesik (Department of Computer Science and Engineering Hankyong National University)
  • Received : 2017.06.03
  • Accepted : 2017.11.28
  • Published : 2018.07.31

Abstract

We introduce some variants of the finite Ramsey theorem. The variants are based on a refinement of homogeneity. In particular, they cover homogeneity, minimal homogeneity, end-homogeneity as special cases. We also show how to obtain upper bounds for the corresponding Ramsey numbers.

Keywords

Ramsey theory;Ramsey numbers;homogeneity

Acknowledgement

Supported by : National Research Foundation of Korea(NRF)

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