Skip to main content
SpringerLink
Log in

The dimension of cycle-free orders

  • Published:
Order Aims and scope Submit manuscript

Abstract

The existence of a four-dimensional cycle-free order is proved. This answers a question of Ma and Spinrad. Two similar problems are also discussed.

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. V. Bouchitte and M. Habid (1989) The calculation of invariants for ordered sets,Algorithms and Order (I. Rival, ed.) Kluwer, 231–279.

  2. B. Dushnik and E. M. Miller (1941) Partially ordered sets,Amer. J. Math. 63, 600–610.

    Google Scholar 

  3. P. C. Fishburn (1985)Interval Orders and Interval Graphs, Wiley, New York.

    Google Scholar 

  4. Z. Füredi, P. Hajnal, V. Rödl and W. T. Trotter (1989) Interval orders and shift graphs, Preprint.

  5. D. Kelly and W. T. Trotter (1982) Dimension theory for ordered sets,Proceedings of Symposium on Ordered Sets (I. Rival, ed.) Reidel, 171–212.

  6. T. H. Ma and J. P. Spinrad (1991) Cycle-free partial orders and chordal comparability graphs,Order 8, 49–61.

    Google Scholar 

  7. I. Rabinovitch (1973) The Dimension Theory of Semiorders and Interval Orders, Ph.D. thesis, Dartmouth College.

  8. W. T. Trotter (1989) Problems and conjectures in the combinatorial theory of ordered sets,Annals of Discrete Math. 41, 401–416.

    Google Scholar 

Download references

Author information

Authors and Affiliations

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

    H. A. Kierstead & W. T. Trotter

  2. Department of Computer Science, Voorhees College, 29042, Denmark, SC, USA

    Jun Qin

Authors
  1. H. A. Kierstead
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. W. T. Trotter
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jun Qin
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by I. Rival

Research partially supported by Office of Naval Research grant N00014-90-J-1206

Research partially supported by the National Science Foundation under grant DMS

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kierstead, H.A., Trotter, W.T. & Qin, J. The dimension of cycle-free orders. Order 9, 103–110 (1992). https://doi.org/10.1007/BF00814403

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00814403

Mathematics Subject Classification (1991)

Key words

Search

Navigation