Skip to main content
SpringerLink
Log in

A splitting property of maximal antichains

  • Published:
Combinatorica Aims and scope Submit manuscript

Abstract

In anydense posetP (and in any Boolean lattice in particular) every maximal antichainS may be partitioned into disjoint subsetsS 1 andS 2, such that the union of the downset ofS 1 with the upset ofS 2 yields the entire poset:D(S 1) ∪U (S 2) =P. To find a similar splitting of maximal antichains in posets is NP-hard in general.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. U. Faigle: Personal communication, (1993).

  2. M. Garey, D. Johnson:Computers and Intractability A Guide to the Theory of NP-Completeness, Freeman, New York (1979).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Bielefeld, P.O. Box 100131, 33501, Bielefeld, Germany

    Rudolf Ahlswede

  2. Centrum voor Wiskunde en Informatica, The Netherlands

    Péter L. Erdős

  3. Mathematical Institute of the Hungarian Academy of Sciences, Budapest, Hungary

    Péter L. Erdős

  4. Department of Computer Science, The University of Alabama in Huntsville, 35899, Huntsville, Alabama, USA

    Niall Graham

Authors
  1. Rudolf Ahlswede
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Péter L. Erdős
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Niall Graham
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Research was partially carried out when the second author visited the first author in Bielefeld and it was partially supported by OTKA grant T016358

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ahlswede, R., Erdős, P.L. & Graham, N. A splitting property of maximal antichains. Combinatorica 15, 475–480 (1995). https://doi.org/10.1007/BF01192520

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01192520

Mathematics Subject Classification (1991)

Search

Navigation