Application of Ramsey Numbers

Question

The definition of Ramsey numbers is the following:

Let $R(a,b)$ be a positive number such that every graph of order at least $R(a,b)$ contains either a clique on $a$ vertices or a stable set on $b$ vertices.

I am working on some extension of Ramsey Numbers. While the study has some theoretical interest, it would be important to know the motivation of these numbers. More specifically I am wondering the (theoretical or practical) applications of Ramsey numbers. For instance, are there any solution methodology for a real life problem that uses Ramsey numbers? Or similarly, are there any proofs of some theorems based on Ramsey numbers?

Answer 1

http://www.cs.umd.edu/~gasarch/ramsey/ramsey.html

Answer 2

In addition to above, http://www.combinatorics.org/Surveys/ds13.pdf also seems to have interesting notes on applications of Ramsey Numbers. Also, I can perceive applications to Genetic Algorithms.