Geodesic
On partitions of hereditary properties of graphs
Discussiones Mathematicae. Graph Theory, Tome 26 (2006) no. 3, pp. 377-387

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In this paper a concept -Ramsey Class of graphs is introduced, where is a class of bipartite graphs. It is a generalization of well-known concept of Ramsey Class of graphs. Some -Ramsey Classes of graphs are presented (Theorem 1 and 2). We proved that ₂, the class of all outerplanar graphs, is not ₁-Ramsey Class (Theorem 3). This results leads us to the concept of acyclic reducible bounds for a hereditary property . For ₂ we found two bounds (Theorem 4). An improvement, in some sense, of that in Theorem is given.
Keywords: hereditary property, acyclic colouring, Ramsey class 
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Borowiecki, Mieczysław; Fiedorowicz, Anna. On partitions of hereditary properties of graphs. Discussiones Mathematicae. Graph Theory, Tome 26 (2006) no. 3, pp. 377-387. http://geodesic.mathdoc.fr/item/DMGT_2006_26_3_a2/