Dualities in full homomorphisms

Authors:
Richard N. Ball;Jaroslav Nešetřil;Aleš Pultr
Affiliations:
Department of Mathematics, University of Denver, Denver, CO 80208, USA;Department of Applied Mathematics, MFF, Charles University, CZ 11800 Praha 1, Malostranské nám. 25, Czech Republic and ITI, MFF, Charles University, CZ 11800 Praha 1, Malostranské n ...;Department of Applied Mathematics, MFF, Charles University, CZ 11800 Praha 1, Malostranské nám. 25, Czech Republic and ITI, MFF, Charles University, CZ 11800 Praha 1, Malostranské n ...
Venue:
European Journal of Combinatorics
Year:
2010

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Abstract

In this paper we study dualities of graphs and, more generally, relational structures with respect to full homomorphisms, that is, mappings that are both edge- and non-edge-preserving. The research was motivated, a.o., by results from logic (concerning first order definability) and Constraint Satisfaction Problems. We prove that for any finite set of objects B (finite relational structures) there is a finite duality with B to the left. It appears that the surprising richness of these dualities leads to interesting problems of Ramsey type; this is what we explicitly analyze in the simplest case of graphs.