Some problems related to Ramsay's theorem

Williams, Edgar Roland (1967) Some problems related to Ramsay's theorem. Masters thesis, Memorial University of Newfoundland.

[English] PDF (Migrated (PDF/A Conversion) from original format: (application/pdf)) - Accepted Version Available under License - The author retains copyright ownership and moral rights in this thesis. Neither the thesis nor substantial extracts from it may be printed or otherwise reproduced without the author's permission. Download (1MB) [English] PDF - Accepted Version Available under License - The author retains copyright ownership and moral rights in this thesis. Neither the thesis nor substantial extracts from it may be printed or otherwise reproduced without the author's permission. (Original Version)

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.

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