Ramsey numbers involving cycles

Abstract

There is a vast amount of literature on Ramsey-type problems starting in 1930 with the original paper of Ramsey [Ram]. Graham, Rothschild and Spencer in their book, Ramsey Theory [GRS] and Soifer in the 2009 The Mathematical Coloring Book, Mathematics of Coloring and the Colorful Life of Its Creators [Soi] present exciting developments in the history, results and people of Ramsey theory. The subject has grown amazingly, in particular with regard to asymptotic bounds for various types of Ramsey numbers (for example, see the survey papers [GrRö; Neš; ChGra2]), but the progress on evaluating the basic numbers themselves has been very unsatisfactory for a long time.