Series-parallel planar ordered sets have pagenumber two

Extended abstract
  • Mohammad Alzohairi
  • Ivan Rival
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1190)


The pagenumber of a series-parallel planar P is at most two. We present an O(n3) algorithm to construct a two-page embedding in the case that it is a lattice. One consequence of independent interest, is a characterization of series-parallel planar ordered sets.


Planar Graph Planar Lattice Linear Extension Page Number Maximal Chain 
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  1. [1]
    F. Bernhart and P. C. Kainen (1979) The book thickness of a graph, Journal of Combinatorial Theory, Series B 27, 320–331.Google Scholar
  2. [2]
    G. Birkhoff (1967) Lattice Theory, American Mathematical Society, Providence, Rhode Island.Google Scholar
  3. [3]
    L. T. Q. Hung (1993) A Planar Poset which Requires four Pages, Ars Combin 35, 291–302Google Scholar
  4. [4]
    H. de Fraysseix, P. O. de Mendez and J. Pach (1995) A Left Search Algorithm for Planar Graphs, Discrete Comput. Geom. 13, 459–468.Google Scholar
  5. [5]
    D. Kelly and I. Rival (1975) Planar lattices, Canad. Journal of Mathematics 27, 636–665.Google Scholar
  6. [6]
    H. M. MacNeille (1937) Partially ordered sets, Trans. Amer. Math. Soc. 42, 416–460.MathSciNetGoogle Scholar
  7. [7]
    R. Nowakowski and A. Parker (1989), Ordered sets, pagenumbers and planarity, Order 6, 209–218.CrossRefGoogle Scholar
  8. [8]
    S. V. Pemmaraju (1992) Exploring the Powers of Stacks and Queues via Graph Layouts, Ph.D. thesis, Virginia Polytechnic Institute and State University at Blacksburg, Virginia.Google Scholar
  9. [9]
    M. M. Sysło (1990) Bounds to the Page Number of Partially Ordered Sets, Graph-theoretic concepts in computer science (Kerkrade, 1989), 181–195, Lecture Notes in Comput. Sci. 411. Springer, Berlin.Google Scholar
  10. [10]
    J. Valdes, R. E. Tarjan and E. L. Lawler (1982) The recognition of seriesparallel digraphs, SIAM J. Computing 11, 298–314.CrossRefGoogle Scholar
  11. [11]
    M. Yannakakis (1989) Embedding planar graphs in four pages, J. Comput. System Sci. 38, 36–67CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Mohammad Alzohairi
    • 1
  • Ivan Rival
    • 2
  1. 1.Department of Mathematics and StatisticsUniversity of OttawaOttawaCanada
  2. 2.Department of Computer ScienceUniversity of OttawaOttawaCanada

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