Some nonstandard Ramsey like applications

AbstractIn this paper, a survey is given of some of the recent research which is related to a particular combinatorial principle namely the Ramsey theorem.One uses very often elementary and less elementary combinatorial facts and it is not important whether one deserves the name ‘principle’ for them. As examples consider the principle of inclusion and exclusion, the pigeonhole principle, counting in two ways, several basic properties of trees etc. It is the author's aim here to show a large variety of applications of the Ramsey theorem. It should be stressed that none of the classical and ‘standard’ applications is mentioned. These can be found in several books and survey articles examples of which are the works of Graham et al. (1980) and Neśetřil and Rödl (1979)