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Computing the dimension ofN-free ordered sets is NP-complete

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Abstract

We show that the problem of deciding whether anN-free ordered set has dimension at most 3 is NP-complete.

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References

  1. M. R. Garey, D. S. Johnson, and L. Stockmeyer (1976) Some simplified NP-complete graph problems,Theor. Comput. Sci. 1, 237–267.

    Article  Google Scholar 

  2. V. Bouchitte and M. Habib (1988) The calculation of invariants for ordered sets, inAlgorithms and Order (ed. I. Rival), Kluwer Academic Publishers, Dordrecht, pp. 231–279.

    Google Scholar 

  3. H. A. Kierstead (1988) Problem 7.1, inAlgorithms and Order (ed. I. Rival), Kluwer Academic Publishers, Dordrecht, p. 489.

    Google Scholar 

  4. R. Kimble (1973) Extremal problems in dimension theory for partially ordered sets, PhD thesis, MIT, Cambridge, Mass.

    Google Scholar 

  5. J. G. Lee, W. P. Liu, R. Nowakowski, and I. Rival, Dimension invariance of subdivisions, preprint.

  6. I. Rival (1983) Optimal linear extensions by interchanging chains,Proc. AMS 89, 387–394.

    Google Scholar 

  7. J. P. Spinrad (1988) Edge subdivision and dimension,Order 5, 143–147.

    Article  Google Scholar 

  8. W. T. Trotter (1981) Stacks and splits of partially ordered sets,Disc. Math. 35, 229–256.

    Article  Google Scholar 

  9. M. Yannakakis (1982) The complexity of the partial order dimension problem,SIAM J. Alg. Disc. Meth. 3, 351–358.

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Arizona State University, 85287, Tempe, AZ, USA

    H. A. Kierstead & S. G. Penrice

Authors
  1. H. A. Kierstead
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  2. S. G. Penrice
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Additional information

Communicated by I. Rival

Both authors supported by Office of Naval Research contract N00014-85K-0494.

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Kierstead, H.A., Penrice, S.G. Computing the dimension ofN-free ordered sets is NP-complete. Order 6, 133–135 (1989). https://doi.org/10.1007/BF02034331

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  • DOI: https://doi.org/10.1007/BF02034331

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