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International Workshop on Graph-Theoretic Concepts in Computer Science

WG 1989: Graph-Theoretic Concepts in Computer Science pp 181–195Cite as

Bounds to the page number of partially ordered sets

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 411))

Abstract

In this paper we initiate study of a new poset invariant, the page number, well-known for graphs. Lower and upper bounds are derived and then they are used to evaluate and to bound the exact value of the page number for some families of posets. Several problems are posed.

This research was partially supported by the grant RP.I.09 from the Institute of Informatics, University of Warsaw.

On leave from Institute of Computer Science, University of Wrocław, Przesmyckiego 20, 51151 Wrocław, Poland.

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References

  1. Bernhart, F., P.C. Kainen, The book thickness of a graph, J. Combin. Theory B 27(1979), 320–321.

    Article  Google Scholar 

  2. Chung, F.R.K., F.T. Leighton, A.L. Rosenberg, Embedding graphs in books: a layout problem with application to VLSI design, SIAM J. Algebraic and Discrete Methods 8(1987), 33–58.

    Google Scholar 

  3. Garey, M.R., D.S. Johnson, G.L. Miller, C.H. Papadimitriou, The complexity of coloring circular arcs and chords, SIAM J. Algebraic and Discrete Methods 1(1980), 216–227.

    Google Scholar 

  4. Golumbic, M.C., Algorithmic Graph Theory and Perfect Graphs, Academic Press, New York 1980.

    Google Scholar 

  5. Habib, M., Comparability invariants, Ann. Discrete Math. 23(1984) 371–386.

    Google Scholar 

  6. Habib, M., R. Moehring, G. Steiner, Computing the bump number is easy, Order 5(1988), 107–129.

    Article  Google Scholar 

  7. Heath, L.S., Algorithms for embedding graphs in books, Ph.D. Dissertation, TR 85-028, Dept. Comput. Sci., Univ. North Carolina at Chapel Hill, 1985.

    Google Scholar 

  8. Kelly, D., Fundamentals of planar ordered sets, Discrete Math. 63(1987), 197–216.

    Article  Google Scholar 

  9. Nowakowski, R., Problems 3.7 and 3.8 in: Rival, I. (ed.), Algorithms and Order, Kluver, Dordrecht 1989, p. 478.

    Google Scholar 

  10. Nowakowski, R., A. Parker, Ordered sets, pagenumbers and planarity, manuscript, 1989.

    Google Scholar 

  11. Wigderson, A., The complexity of the Hamiltonian circuit problem for maximal planar graphs, Report 298, EECS Dept. Princeton University, 1982.

    Google Scholar 

  12. Yannakakis, M., Four pages are necessary and sufficient for planar graphs, in: Proceedings of the 18th ACM Symposium on Theory of Computing, 1986, pp. 104–108.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Technische Universitaet Berlin, FB 3 — Mathematik, Str. des 17. Juni 135, 1000, Berlin 12

    Maciej M. Sysło (A Fellow of the Alexander von Humboldt-Stiftung (Bonn)

Authors
  1. Maciej M. Sysło
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Editor information

Manfred Nagl

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© 1990 Springer-Verlag Berlin Heidelberg

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Sysło, M.M. (1990). Bounds to the page number of partially ordered sets. In: Nagl, M. (eds) Graph-Theoretic Concepts in Computer Science. WG 1989. Lecture Notes in Computer Science, vol 411. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-52292-1_13

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  • DOI: https://doi.org/10.1007/3-540-52292-1_13

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-52292-8

  • Online ISBN: 978-3-540-46950-6

  • eBook Packages: Springer Book Archive

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