Threshold functions for asymmetric Ramsey properties with respect to vertex colorings

In this note we investigate Ramsey properties of random graphs. The threshold functions for symmetric Ramsey properties with respect to vertex colorings were determined by Łuczak, Ruciński, and Voigt [6]. As a generalization of this problem we consider asymmetric Ramsey properties and establish the values of the threshold functions. Furthermore, we investigate canonical colorings. © 1996 John Wiley & Sons, Inc.