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On the Homomorphism Order of Labeled Posets

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Abstract

Partially ordered sets labeled with k labels (k-posets) and their homomorphisms are examined. We give a representation of directed graphs by k-posets; this provides a new proof of the universality of the homomorphism order of k-posets. This universal order is a distributive lattice. We investigate some other properties, namely the infinite distributivity, the computation of infinite suprema and infima, and the complexity of certain decision problems involving the homomorphism order of k-posets. Sublattices are also examined.

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Authors and Affiliations

  1. School of Engineering, Zurich University of Applied Sciences, Technikumstrasse 9, 8401, Winterthur, Switzerland

    Léonard Kwuida

  2. Faculty of Science, Technology and Communication, University of Luxembourg, 6, rue Richard Coudenhove-Kalergi, 1359, Luxembourg, Luxembourg

    Erkko Lehtonen

Authors
  1. Léonard Kwuida
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  2. Erkko Lehtonen
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Correspondence to Erkko Lehtonen.

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Kwuida, L., Lehtonen, E. On the Homomorphism Order of Labeled Posets. Order 28, 251–265 (2011). https://doi.org/10.1007/s11083-010-9169-x

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  • DOI: https://doi.org/10.1007/s11083-010-9169-x

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