Some problems related to Ramsay's theorem

Abstract

In 1930, P.P. Ramsay published a paper containing a combinatorial theorem which has since then become very well known and has given rise to an extensive literature. Most of the research which has arisen from Ramsay's Theorem, has dealt with the problem of finding upper and lower bounds for the so called Ramsay numbers. In addition, some exact values of these numbers have been determined and some applications of Ramsay's Theorem have been given. -- In this thesis, we survey some of the research which has been done. In addition, some new results have been obtained. These results yield a better lower bound for certain classes of Ramsay numbers, than any of those that have been obtained up to the present time.