Communications of the
Korean Mathematical Society CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024
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Commun. Korean Math. Soc. 2018; 33(3): 1001-1011

Online first article June 1, 2018      Printed July 31, 2018

https://doi.org/10.4134/CKMS.c170234

Copyright © The Korean Mathematical Society.

Refinement of Homogeneity and Ramsey numbers

Hwajeong Kim, Gyesik Lee

Hannam University, Hankyong National University

Abstract

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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

MSC numbers: Primary 05D10, 05C55, 68R05

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