# 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} }

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…

## 2 Citations

Recent developments in graph Ramsey theory

- MathematicsSurveys in Combinatorics
- 2015

There has been a great deal of recent progress on the study of Ramsey numbers and their variants, spurred on by the many advances across extremal combinatorics.

Ramsey Theory in the Work of Paul Erdős

- PhilosophyThe Mathematics of Paul Erdős II
- 2013

This paper will attempt to demonstrate that Ramsey’s theorem was not discovered by P. Erdős, but that Ramsey theory was created largely by him.

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