Advertisement

A New Approach for Contact Graph Representations and Its Applications

  • Yi-Jun Chang
  • Hsu-Chun Yen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9214)

Abstract

A contact graph representation is a classical graph drawing style in which vertices are represented by geometric objects such that edges correspond to contacts between objects. Based on a characterization of stretchable systems of pseudo segments, we present a new approach for constructing a wide range of contact graph representations. Using Courcelle’s theorem, some useful fixed-parameter tractability results are derived. Our approach can also be applied to giving quick proofs for some existing results of contact graph representations. We feel that the technique developed in the paper gives new insight to the study of contact representations of plane graphs.

Keywords

Plane Graph Contact System Outer Face Contact Representation Outerplanar Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Aerts, N., Felsner, S.: Straight line triangle representations. In: Wismath, S., Wolff, A. (eds.) GD 2013. LNCS, vol. 8242, pp. 119–130. Springer, Heidelberg (2013) CrossRefGoogle Scholar
  2. 2.
    Alam, M.J., Biedl, T., Felsner, S., Kaufmann, M., Kobourov, S.G., Ueckert, T.: Computing Cartograms with Optimal Complexity. Discrete & Computational Geometry 50(3), 784–810 (2013)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Courcelle, B.: The monadic second-order logic of graphs. I. Recognizable sets of finite graphs. Information and Computation 85(1), 12–75 (1990)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Courcelle, B., Engelfriet, J.: Graph Structure and Monadic Second-Order Logic: A Language-Theoretic Approach. Cambridge University Press (2012)Google Scholar
  5. 5.
    De Fraysseix, H., de Mendez, P.O.: Barycentric systems and stretchability. Discrete Applied Mathematics 155(9), 1079–1095 (2007)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Downey, R., Fellows, M.: Fundamentals of Parameterized Complexity. Springer (2013)Google Scholar
  7. 7.
    Duncan, C., Gansner, E., Hu, Y., Kaufmann, M., Kobourov, S.: Optimal Polygonal Representation of Planar Graphs. Algorithmica 63(3), 672–691 (2012)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Evans, W., Felsner, S., Kaufmann, M., Kobourov, S.G., Mondal, D., Nishat, R.I., Verbeek, K.: Table cartograms. In: Bodlaender, H.L., Italiano, G.F. (eds.) ESA 2013. LNCS, vol. 8125, pp. 421–432. Springer, Heidelberg (2013) CrossRefGoogle Scholar
  9. 9.
    Fowler, J.J.: Strongly-connected outerplanar graphs with proper touching triangle representations. In: Wismath, S., Wolff, A. (eds.) GD 2013. LNCS, vol. 8242, pp. 155–160. Springer, Heidelberg (2013) CrossRefGoogle Scholar
  10. 10.
    Gansner, E.R., Hu, Y., Kobourov, S.G.: On touching triangle graphs. In: Brandes, U., Cornelsen, S. (eds.) GD 2010. LNCS, vol. 6502, pp. 250–261. Springer, Heidelberg (2011) CrossRefGoogle Scholar
  11. 11.
    Kobourov, S.G., Mondal, D., Nishat, R.I.: Touching triangle representations for 3-connected planar graphs. In: Didimo, W., Patrignani, M. (eds.) GD 2012. LNCS, vol. 7704, pp. 199–210. Springer, Heidelberg (2013) CrossRefGoogle Scholar
  12. 12.
    Koebe, P.: Kontaktprobleme der konformen Abbil-dung. Ber. Verh. Sachs. Akademie der Wissenschaften Leipzig, Math.-Phys. Klasse 88, 141–164 (1936)Google Scholar
  13. 13.
    Ueckerdt, T.: Geometric Representations of Graphs with low Polygonal Complexity. PhD thesis, Technische Universität Berlin (2011)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of Electrical EngineeringNational Taiwan UniversityTaipeiTaiwan, Republic of China

Personalised recommendations