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On complexity of some chain and antichain partition problems

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Graph-Theoretic Concepts in Computer Science (WG 1991)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 570))

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Abstract

In the paper we deal with computational complexity of a problem C k (respectively A k ) of a partition of an ordered set into minimum number of at most k-element chains (resp. antichains). We show that C k , k ≥ 3, is NP-complete even for N-free ordered sets of length at most k, C k and A k are polynomial for series-paralel orders and A k is polynomial for interval orders. We also consider related problems for graphs.

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Authors and Affiliations

  1. Institute of Mathematics, Warsaw University of Technology, 00-661, Warsaw, Poland

    Zbigniew Lonc

Authors
  1. Zbigniew Lonc
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Editor information

Gunther Schmidt Rudolf Berghammer

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© 1992 Springer-Verlag Berlin Heidelberg

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Lonc, Z. (1992). On complexity of some chain and antichain partition problems. In: Schmidt, G., Berghammer, R. (eds) Graph-Theoretic Concepts in Computer Science. WG 1991. Lecture Notes in Computer Science, vol 570. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-55121-2_9

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  • DOI: https://doi.org/10.1007/3-540-55121-2_9

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55121-8

  • Online ISBN: 978-3-540-46735-9

  • eBook Packages: Springer Book Archive

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