# Two extensions of Ramsey's theorem

@article{Conlon2011TwoEO,
title={Two extensions of Ramsey's theorem},
author={David Conlon and Jacob Fox and Benny Sudakov},
journal={ArXiv},
year={2011},
volume={abs/1112.1548}
}
• Published 7 December 2011
• Mathematics
• ArXiv
Ramsey's theorem, in the version of Erd\H{o}s and Szekeres, states that every 2-coloring of the edges of the complete graph on {1, 2,...,n} contains a monochromatic clique of order 1/2\log n. In this paper, we consider two well-studied extensions of Ramsey's theorem. Improving a result of R\"odl, we show that there is a constant $c>0$ such that every 2-coloring of the edges of the complete graph on \{2, 3,...,n\} contains a monochromatic clique S for which the sum of 1/\log i over all vertices…
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