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Path homomorphisms

Published online by Cambridge University Press:  24 October 2008

Jaroslav Nešetřil  and
Xuding Zhu
Jaroslav Nešetřil
Affiliation:
Department of Applied Mathematics, Charles University, Prague
Xuding Zhu
Affiliation:
Department of Mathematics and Statistics, Simon Fraser University, Burnaby, BC V5A 1S6, Canada
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Abstract

We investigate homomorphisms between finite oriented paths. We demonstrate the surprising richness of this perhaps simplest case of homomorphism between graphs by proving the density theorem for oriented paths. As a consequence every two dimensional countable poset is represented finite paths and their homomorphisms, and every finite dimensional poset is represented finite oriented trees and their homomorphisms. We then consider related problems of universal representability and extendability and on-line representability.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 120 , Issue 2 , August 1996 , pp. 207 - 220
Copyright
Copyright © Cambridge Philosophical Society 1996

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