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Discussiones Mathematicae Graph Theory 22(1) (2002) 183-192
DOI: https://doi.org/10.7151/dmgt.1167

ON GENERATING SETS OF INDUCED-HEREDITARY PROPERTIES

 Gabriel Semanišin

 Department of Geometry and Algebra
Faculty of Science, P.J. Safárik University
Jesenná 5, 041 54 Košice, Slovak Republic
e-mail: semanisin@science.upjs.sk

Abstract

A natural generalization of the fundamental graph vertex-colouring problem leads to the class of problems known as generalized or improper colourings. These problems can be very well described in the language of reducible (induced) hereditary properties of graphs. It turned out that a very useful tool for the unique determination of these properties are generating sets. In this paper we focus on the structure of specific generating sets which provide the base for the proof of The Unique Factorization Theorem for induced-hereditary properties of graphs.

Keywords: induced-hereditary property of graphs, additivity, reducibility, generating sets, maximal graphs, unique factorization.

2000 Mathematics Subject Classification: 05C15, O5C75.

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Received 31 July 2000
Revised 21 May 2001