Universal partial order represented by means of oriented trees and other simple graphs

Authors:
Jan Hubička;Jaroslav Nešetřil
Affiliations:
Department of Applied Mathematics and Institute of Theoretical Computer sciences (IT1), Charles University, Malostranské nám. 25, 11800 Praha, Czech Republic;Department of Applied Mathematics and Institute of Theoretical Computer sciences (IT1), Charles University, Malostranské nám. 25, 11800 Praha, Czech Republic
Venue:
European Journal of Combinatorics
Year:
2005

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Abstract

We present several simple representations of universal partially ordered sets and use them for the proof of universality of the class of oriented trees ordered by the graph homomorphisms. This (which we believe to be a surprising result) solves several open problems. It implies for example universality of cubic planar graphs. This is in sharp contrast with representing even groups (and monoids) by automorphisms (and endomorphisms) of a bounded degree and planar graph. Thus universal partial orders (thin categories) are representable by much simpler structures than categories in general.