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The Homomorphism Structure of Classes of Graphs

Published online by Cambridge University Press:  01 January 1999

JAROSLAV NEšETŘIL
Affiliation:
Department of Applied Mathematics, Charles University, Malostranské nám. 25, 118 00 Prague, Czech Republic (e-mail: [email protected])

Abstract

We consider three aspects of homomorphisms of graphs and hypergraphs which are related to the structure of colour classes: (1) density, (2) the fractal property and (3) the generation of colour classes. In particular, we prove a density theorem for hypergraphs and show that, for connected oriented graphs, all jumps are balanced (and give an example to show that connectivity is needed here). We also show that a Hajós-type theorem holds for any colour class of undirected graphs, thus providing further evidence of the well-known ‘non-effective’ character of Hajós' theorem.

Type
Research Article
Copyright
© 1999 Cambridge University Press

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