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On the Orthogonal Drawing of Outerplanar Graphs

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Computing and Combinatorics (COCOON 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3106))

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Abstract

In this paper we show that an outerplanar graph G with maximum degree at most 3 has a 2-D orthogonal drawing with no bends if and only if G contains no triangles. We also show that an outerplanar graph G with maximum degree at most 6 has a 3-D orthogonal drawing with no bends if and only if G contains no triangles.

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References

  1. Battista, G., Liotta, G., Vargiu, F.: Spirality and optimal orthogonal drawings. SIAM J. Comput. 27, 1764–1811 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  2. Biedl, T., Kant, G.: A better heuristic for orthogonal graph drawings. In: van Leeuwen, J. (ed.) ESA 1994. LNCS, vol. 855, pp. 24–35. Springer, Heidelberg (1994)

    Chapter  Google Scholar 

  3. Eades, P., Strik, C., Whitesides, S.: The techniques of komolgorov and bardzin for three-dimensional orthogonal graph drawings. Information Processing Letters 60, 97–103 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  4. Eades, P., Symvonis, A., Whitesides, S.: Three-dimensional orthogonal graph drawing algorithms. Discrete Applied Mathmatics 103, 55–87 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  5. Garg, A., Tamassia, R.: On the computational complexity of upward and rectilinear planarity testing. SIAM J. Comput. 31, 601–625 (1995)

    Article  MathSciNet  Google Scholar 

  6. Kant, G.: Drawing planar graphs using the canonical ordering. Algorithmica 16, 4–32 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  7. Liu, Y., Morgana, A., Simeone, B.: A linear algorithm for 2-bend embeddings of planar graphs in the two-dimensional grid. Discrete Applied Mathmatics 81, 69–91 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  8. Papakostas, A., Tollis, I.G.: Algorithm for incremental orthogonal graph drawing in three dimensions. J. Graph Algorithms and Applications 3, 81–115 (1999)

    MATH  MathSciNet  Google Scholar 

  9. Rahman, M.S., Naznin, M., Nishizeki, T.: Orthogonal drawing of plane graphs without bends. In: Mutzel, P., Jünger, M., Leipert, S. (eds.) GD 2001. LNCS, vol. 2265, pp. 392–406. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  10. Wood, D.R.: Optimal three-dimensional orthogonal graph drawing in the general position model. Theoretical Computer Science 299, 151–178 (2003)

    Article  MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Dept. of Communications and Integrated Systems, Graduate School of Science and Engineering, Tokyo Institute of Technology, Tokyo, 152-8552, Japan

    Kumiko Nomura, Satoshi Tayu & Shuichi Ueno

Authors
  1. Kumiko Nomura
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  2. Satoshi Tayu
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  3. Shuichi Ueno
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Editor information

Editors and Affiliations

  1. Division of Computer Science, Korea Advanced Institute of Science and Technology, Daejeon, Republic of Korea

    Kyung-Yong Chwa

  2. Cheriton School of Computer Science, University of Waterloo, Waterloo, Ontario, Canada

    J. Ian J. Munro

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© 2004 Springer-Verlag Berlin Heidelberg

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Nomura, K., Tayu, S., Ueno, S. (2004). On the Orthogonal Drawing of Outerplanar Graphs. In: Chwa, KY., Munro, J.I.J. (eds) Computing and Combinatorics. COCOON 2004. Lecture Notes in Computer Science, vol 3106. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27798-9_33

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  • DOI: https://doi.org/10.1007/978-3-540-27798-9_33

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22856-1

  • Online ISBN: 978-3-540-27798-9

  • eBook Packages: Springer Book Archive

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