Discussiones Mathematicae Graph Theory 26(3) (2006) 377-387
doi: 10.7151/dmgt.1330

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ON PARTITIONS OF HEREDITARY PROPERTIES OF GRAPHS

Mieczysław Borowiecki and Anna Fiedorowicz

Faculty of Mathematics, Computer Science
and Econometrics, University of Zielona Góra
Prof. Z. Szafrana 4a, 65-516 Zielona Góra, Poland
e-mail: M.Borowiecki@wmie.uz.zgora.pl
e-mail: A.Fiedorowicz@wmie.uz.zgora.pl

Abstract

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 well-known 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 D 1-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 is given.

Keywords: hereditary property, acyclic colouring, Ramsey class.

2000 Mathematics Subject Classification: 05C15, 05C75.

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Received 11 January 2006
Revised 21 September 2006