On partitions of hereditary properties of graphs

In this paper a concept Q-Ramsey Class of graphs is introduced, where Q is a class of bipartite graphs. It is a generalization of wellknown concept of Ramsey Class of graphs. Some Q-Ramsey Classes of graphs are presented (Theorem 1 and 2). We proved that T 2, the class of all outerplanar graphs, is not D1-Ramsey Class (Theorem 3). This results leads us to the concept of acyclic reducible bounds for a hereditary property P. For T 2 we found two bounds (Theorem 4). An improvement, in some sense, of that in Theorem 5 is given.