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Canonical Vertex Partitions

Published online by Cambridge University Press:  03 December 2003

N. W. Sauer
N. W. Sauer*
Affiliation:
Department of Mathematics and Statistics, University of Calgary, 2500 University Drive NW, Calgary, Alberta, T2N 1N4, Canada
*
(e-mail: nsauer@math.ucalgary.ca)
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Abstract

Let σ be a finite relational signature, let be a set of finite complete relational structures of signature σ, and let be the countable homogeneous relational structure of signature σ which does not embed any of the structures in .

When σ consists of at most binary relations and is finite, the vertex partition behaviour of is completely analysed, in the sense that it is shown that a canonical partition exists and the size of this partition in terms of the structures in is determined. If is infinite some results are obtained, but a complete analysis is still missing.

Some general results are presented which are intended to be used in further investigations when σ contains relational symbols of arity larger than two or when the set of bounds is infinite.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 12 , Issue 5-6: This issue contains volume twelve, parts five and six , November 2003 , pp. 671 - 704
Copyright
Copyright © Cambridge University Press 2003

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Footnotes

†

Supported by NSERC of Canada grant # 691325