The classical problem in Ramsey theory is the party problem, which asks the minimum number of guests that must be invited so that at least
m will know each other (i.e., there exists a clique of order
m) or at least
n will not know each other (i.e., there exists an independent set of order
R(m,n) is called a Ramsey number.
There seems to be a slew of research in the field. What are some real world applications? For example, I read in one place that circuit/network routing would be a good one. But how why is that? Does anyone know of any other real world applications?