A splitting property of maximal antichains

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.

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References

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

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

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

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Mathematics Subject Classification (1991)

  • 05 D 05
  • 06 A 07