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On the Number of Upward Planar Orientations of Maximal Planar Graphs

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Part of the book series:Lecture Notes in Computer Science ((LNTCS,volume 7676))

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Abstract

We consider the problem of determining the maximum and the minimum number of upward planar orientations a maximal planar graph can have. We show thatn-vertex maximal planar graphs have at least Ω(n ·1.189n) and at mostO(n ·4n) upward planar orientations. Moreover, there existn-vertex maximal planar graphs having as few asO(n ·2n) upward planar orientations andn-vertex maximal planar graphs having Ω(2.599n) upward planar orientations.

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References

  1. Bertolazzi, P., Di Battista, G., Liotta, G., Mannino, C.: Upward drawings of triconnected digraphs. Algorithmica 12(6), 476–497 (1994)

    Article MathSciNet MATH  Google Scholar 

  2. Buchin, K., Schulz, A.: On the Number of Spanning Trees a Planar Graph Can Have. In: de Berg, M., Meyer, U. (eds.) ESA 2010, Part I. LNCS, vol. 6346, pp. 110–121. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  3. de Fraysseix, H., de Mendez, P.O., Rosenstiehl, P.: Bipolar orientations revisited. Discr. Appl. Math. 56(2-3), 157–179 (1995)

    Article MATH  Google Scholar 

  4. Di Battista, G., Tamassia, R.: Algorithms for plane representations of acyclic digraphs. Theor. Comput. Sci. 61, 175–198 (1988)

    Article MATH  Google Scholar 

  5. Fusy, E., Poulalhon, D., Schaeffer, G.: Bijective counting of plane bipolar orientations. Elec. Notes Discr. Math. 29, 283–287 (2007)

    Article  Google Scholar 

  6. Garg, A., Tamassia, R.: On the computational complexity of upward and rectilinear planarity testing. SIAM J. Comput. 31(2), 601–625 (2001)

    Article MathSciNet MATH  Google Scholar 

  7. Graham, R.L., Yao, A.C., Yao, F.F.: Information bounds are weak in the shortest distance problem. J. ACM 27(3), 428–444 (1980)

    Article MathSciNet MATH  Google Scholar 

  8. Kahale, N., Schulman, L.J.: Bounds on the chromatic polynomial and on the number of acyclic orientations of a graph. Combinatorica 16(3), 383–397 (1996)

    Article MathSciNet MATH  Google Scholar 

  9. Kelly, D.: Fundamentals of planar ordered sets. Disc. Math. 63(2-3), 197–216 (1987)

    Article MATH  Google Scholar 

  10. Manber, U., Tompa, M.: The effect of number of hamiltonian paths on the complexity of a vertex-coloring problem. SIAM J. Comput. 13(1), 109–115 (1984)

    Article MathSciNet MATH  Google Scholar 

  11. Mehlhorn, K.: Data Structures and Algorithms: Multi-dimensional Searching and Computational Geometry, vol. 3. Springer (1984)

    Google Scholar 

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Author information

Authors and Affiliations

  1. School of Information Technologies, The University of Sydney, Australia

    Fabrizio Frati & Joachim Gudmundsson

  2. Institute of Theoretical Computer Science, ETH Zurich, Switzerland

    Emo Welzl

Authors
  1. Fabrizio Frati

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  2. Joachim Gudmundsson

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  3. Emo Welzl

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Editor information

Editors and Affiliations

  1. Department of Computer Science and Information Engineering, National Taiwan University, 1 Roosevelt Road, Section 4, 106, Taipei, Taiwan

    Kun-Mao Chao

  2. Institute of Information Science, Academia Sinica, 128 Academia Road, Section 2, 115, Taipei, Taiwan

    Tsan-sheng Hsu

  3. Department of Computer Science and Engineering, National Chung Hsing University, 250 Kuo Kuang Road, 402, Taichung, Taiwan

    Der-Tsai Lee

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© 2012 Springer-Verlag Berlin Heidelberg

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Frati, F., Gudmundsson, J., Welzl, E. (2012). On the Number of Upward Planar Orientations of Maximal Planar Graphs. In: Chao, KM., Hsu, Ts., Lee, DT. (eds) Algorithms and Computation. ISAAC 2012. Lecture Notes in Computer Science, vol 7676. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35261-4_44

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Chapter
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Price includes VAT (Japan)
  • Available as PDF
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Softcover Book
JPY 7149
Price includes VAT (Japan)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide -see info

Tax calculation will be finalised at checkout

Purchases are for personal use only


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