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22nd Cumberland Conference on Combinatorics, Graph Theory and Computing
May 21-23, 2009
Western Kentucky University
Bowling Green, KY, USA

Organizers
Bela Csaba, Chair; Mustafa Atici; Robert Crawford; Claus Ernst; Dominic Lanphier; Attila Por

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Some Ramsey Results and Conjectures
by
Richard H. Schelp
University of Memphis

Two different types of Ramsey problems will be discussed with some results and many unanswered questions. The first involves the concept of Ramsey saturated (unsaturated) graphs. A graph is said to be Ramsey saturated if the Ramsey number r(G+e, G+e) > r(G, G) for all e, where e is any edge in the complement G, and Ramsey unsaturated otherwise. Graphs which are Ramsey saturated are precisely those which are edge maximal for a given Ramsey number. The second type discussed involves several problems of the following type. For odd n the two edge coloring of the complete 5-partite multipartite K(n-1)/2, (n-1)/2, (n-1)/2, (n-1)/2, 1 contains a monochromatic cycle Cn on n vertices. The truth of this is best possible and generalizes the fact that the Ramsey number of the odd n-cycle is r(Cn, Cn) = 2n-1.

Date received: April 14, 2009

Copyright © 2009 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cayq-19.