Drawing Series-Parallel Graphs on Restricted Integer 3D Grids

  • Emilio Di Giacomo
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2912)


A k-track drawing is a crossing-free 3D straight-line grid drawing of a graph G on a set of k parallel lines called tracks. The minimum value of k for which G admits a k-track drawing is called the track number of G. In the existing literature a lower bound of five and an upper bound of fifteen are known for the track number of series-parallel graph. In this paper we reduce this gap for a large subclass of series-parallel graph for which the lower bound remains five but we show an upper bound of eight. We also describe a linear time drawing algorithm that computes a 3D straight-line grid drawing of these graphs in volume 4 × 4 × 2n.


  1. 1.
    Chung, F.R.K., Leighton, F.T., Rosenberg, A.: Embedding graphs in books: Ala yout problem with applications to VLSI design. SIAM J. on Alg. and Disc. Methods 8, 33–58 (1987)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Di Battista, G., Eades, P., Tamassia, R., Tollis, I.G.: Graph Drawing. Prentice Hall, Upper Saddle River (1999)MATHGoogle Scholar
  3. 3.
    Di Battista, G., Tamassia, R.: On-line maintenance of triconnected components with SPQR-trees. Algorithmica 15(4), 302–318 (1996)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Di Giacomo, E., Liotta, G., Meijer, H.: 3D straight-line drawings of k-trees (submitted for publication)Google Scholar
  5. 5.
    Di Giacomo, E., Liotta, G., Wismath, S.K.: Drawing series-parallel graphs on a box. In: Proc. CCCG 2002 (2002)Google Scholar
  6. 6.
    Dujmović, V., Morin, P., Wood, D.: Pathwidth and three-dimensional straight line grid drawings of graphs. In: Goodrich, M.T., Kobourov, S.G. (eds.) GD 2002. LNCS, vol. 2528, pp. 42–53. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  7. 7.
    Dujmović, V., Wood, D.R.: Tree-partitions of k-trees with application in graph layout. In: Bodlaender, H.L. (ed.) WG 2003. LNCS, vol. 2880, pp. 205–217. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  8. 8.
    Felsner, S., Liotta, G., Wismath, S.K.: Straight line drawings on restricted integer grids in two and three dimensions. In: Mutzel, P., Jünger, M., Leipert, S. (eds.) GD 2001. LNCS, vol. 2265, pp. 328–342. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  9. 9.
    Wood, D.R.: Queue layouts, tree-width, and three-dimensional graph drawing. In: Agrawal, M., Seth, A.K. (eds.) FSTTCS 2002. LNCS, vol. 2556, pp. 348–359. Springer, Heidelberg (2002)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Emilio Di Giacomo
    • 1
  1. 1.Dipartimento di Ingegneria Elettronica e dell’InformazioneUniversitá degli Studi di PerugiaPerugiaItaly

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