## CARDINALITY OF A MINIMAL FORBIDDEN GRAPH FAMILY FOR REDUCIBLE ADDITIVE HEREDITARY GRAPH PROPERTIES

Ewa Drgas-Burchardt

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

## Abstract

An additive hereditary graph property is any class of simple graphs, which is closed under isomorphisms unions and taking subgraphs. Let La denote a class of all such properties. In the paper, we consider H-reducible over La properties with H being a fixed graph. The finiteness of the sets of all minimal forbidden graphs is analyzed for such properties.

Keywords: hereditary graph property, lattice of additive hereditary graph properties, minimal forbidden graph family, join in the lattice, reducibility.

2000 Mathematics Subject Classification: 05C75, 05C15, 05C35.

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Received 21 December 2007
Revised 26 September 2008
Accepted 1 December 2008