Another Definition for Ramsey Numbers

We introduce an idea or a concept of restricted coexistence. By the restricted coexistence, the Ramsey number R(p,q) is defined equivalently as r(p-1,q), that is, R(p,q)=r(p-1,q), where r(p-1,q) is a least integer that has coexistence restricted to the parameters p-1,q with q ges p ges 2. From this, some basic properties about Ramsey numbers are obtained, for instance, R(p,q)>R(p-1,q+1), where p,q are integers with qgespges3, and so on.