ArticleOriginal scientific text
Title
On partitions of hereditary properties of graphs
Authors 1, 1
Affiliations
- Faculty of Mathematics, Computer Science, and Econometrics, University of Zielona Góra, Prof. Z. Szafrana 4a, 65-516 Zielona Góra, Poland
Abstract
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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Pages:
377-387
Main language of publication
English
Received
2006-01-11
Accepted
2006-09-21
Published
2006
DOI: 10.7151/dmgt.1330
Exact and natural sciences