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Homomorphism-Homogeneous Relational Structures

Published online by Cambridge University Press:  03 January 2006

PETER J. CAMERON  and
JAROSLAV NEšETŘIL
PETER J. CAMERON
Affiliation:
School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, London E1 4NS, UK (e-mail: p.j.cameron@qmul.ac.uk)
JAROSLAV NEšETŘIL
Affiliation:
Department of Applied Mathematics and Institute of Theoretical Computer Sciences, Charles University, Malostranské Nám. 25, 11800 Praha, Czech Republic (e-mail: nesetril@kam.mff.cuni.cz)
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Abstract

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We study relational structures (especially graphs and posets) which satisfy the analogue of homogeneity but for homomorphisms rather than isomorphisms. The picture is rather different. Our main results are partial characterizations of countable graphs and posets with this property; an analogue of Fraïssé's theorem; and representations of monoids as endomorphism monoids of such structures.

Information

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 15 , Issue 1-2 , January 2006 , pp. 91 - 103
Copyright
2006 Cambridge University Press