No-Bend Orthogonal Drawings of Subdivisions of Planar Triconnected Cubic Graphs

  • Md. Saidur Rahman
  • Noritsugu Egi
  • Takao Nishizeki
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2912)

Abstract

A plane graph is a planar graph with a fixed embedding. In a no-bend orthogonal drawing of a plane graph, each vertex is drawn as a point and each edge is drawn as a single horizontal or vertical line segment. A planar graph is said to have a no-bend orthogonal drawing if at least one of its plane embeddings has a no-bend orthogonal drawing. In this paper we consider a class of planar graphs, called subdividions of planar triconnected cubic graphs, and give a linear-time algorithm to examine whether such a planar graph G has a no-bend orthogonal drawing and to find one if G has.

References

  1. [DLV98]
    Di Battista, G., Liotta, G., Vargiu, F.: Spirality and optimal orthogonal drawings. SIAM J. Comput. 27(6), 1764–1811 (1998)MATHCrossRefMathSciNetGoogle Scholar
  2. [GT01]
    Garg, A., Tamassia, R.: On the computational complexity of upward and rectilinear planarity testing. SIAM J. Comput. 31(2), 601–625 (2001)MATHCrossRefMathSciNetGoogle Scholar
  3. [NC88]
    Nishizeki, T., Chiba, N.: Planar Graphs: Theory and Algorithms. North-Holland, Amsterdam (1988)MATHGoogle Scholar
  4. [RN02]
    Rahman, M.S., Nishizeki, T.: Bend-minimum orthogonal drawings of plane 3-graphs. In: Kučera, L. (ed.) WG 2002. LNCS, vol. 2573, pp. 265–276. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  5. [RNG02]
    Rahman, M.S., Nishizeki, T., Ghosh, S.: Rectangular drawings of planar graphs. In: Goodrich, M.T., Kobourov, S.G. (eds.) GD 2002. LNCS, vol. 2528, pp. 244–255. Springer, Heidelberg (2002); Also Journal of Algorithms (to appear)CrossRefGoogle Scholar
  6. [RNN00]
    Rahman, M.S., Nakano, S., Nishizeki, T.: Box-rectangular drawings of plane graphs. Journal of Algorithms 37, 363–398 (2000)MATHCrossRefMathSciNetGoogle Scholar
  7. [RNN02]
    Rahman, M.S., Naznin, M., Nishizeki, T.: Orthogonal drawings of plane graphs without bends. In: Mutzel, P., Jünger, M., Leipert, S. (eds.) GD 2001. LNCS, vol. 2265, pp. 392–406. Springer, Heidelberg (2002); Also Journal of Graph Alg. and Appl. (to appear)CrossRefGoogle Scholar
  8. [RNN99]
    Rahman, M.S., Nakano, S., Nishizeki, T.: A linear algorithm for bendoptimal orthogonal drawings of triconnected cubic plane graphs. Journal of Graph Alg. and Appl. 3(4), 31–62 (1999), http://www.cs.brown.edu/publications/jgaa/ MATHMathSciNetGoogle Scholar
  9. [S84]
    Storer, J.: On minimum node-cost planar embeddings. Networks 14, 181–212 (1984)MATHCrossRefMathSciNetGoogle Scholar
  10. [T87]
    Tamassia, R.: On embedding a graph in the grid with the minimum number of bends. SIAM J. Comput. 16, 421–444 (1987)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Md. Saidur Rahman
    • 1
  • Noritsugu Egi
    • 1
  • Takao Nishizeki
    • 1
  1. 1.Graduate School of Information SciencesTohoku UniversitySendaiJapan

Personalised recommendations