The nondensity function and generalized Ramsey numbers

A graph $G$ possesses the $(p, q)$-property if each its subgraph with $p$ vertices contains an empty subgraph with $q$ vertices. The independence function $p(q,G)$ is equal to the least $p$ such that the graph $G$ possesses the $(p,q)$-property, $q\ge2$. We consider the independence function and generalized Ramsey numbers for various classes of graphs.
This research was supported by the Russian Foundation for Basic Research, grant 96-01-01054.