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International Computing and Combinatorics Conference

COCOON 2012: Computing and Combinatorics pp 311–322Cite as

Multilevel Drawings of Clustered Graphs

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7434))

Abstract

The cluster adjacency graph of a flat clustered graph C(G,T) is the graph A whose vertices are the clusters in T and whose edges connect clusters containing vertices that are adjacent in G. A multilevel drawing of a clustered graph C consists of a straight-line c-planar drawing of C in which the clusters are drawn as convex regions and of a straight-line planar drawing of A such that each vertex a ∈ A is drawn in the cluster corresponding to a and such that no edge (a 1,a 2) ∈ A intersects any cluster different from a 1 and a 2. In this paper, we show that every c-planar flat clustered graph admits a multilevel drawing.

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References

  1. Angelini, P., Frati, F., Kaufmann, M.: Straight-line rectangular drawings of clustered graphs. Discrete & Computational Geometry 45(1), 88–140 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  2. Di Battista, G., Drovandi, G., Frati, F.: How to draw a clustered tree. J. Discrete Algorithms 7(4), 479–499 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  3. Di Battista, G., Frati, F.: Efficient c-planarity testing for embedded flat clustered graphs with small faces. J. Graph Alg. Appl. 13(3), 349–378 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  4. Eades, P., Feng, Q.: Multilevel Visualization of Clustered Graphs. In: DiBattista, G. (ed.) GD 1997. LNCS, vol. 1353, pp. 101–112. Springer, Heidelberg (1997)

    Chapter  Google Scholar 

  5. Eades, P., Feng, Q., Lin, X., Nagamochi, H.: Straight-line drawing algorithms for hierarchical graphs and clustered graphs. Algorithmica 44(1), 1–32 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  6. Eades, P., Feng, Q., Nagamochi, H.: Drawing clustered graphs on an orthogonal grid. J. Graph Alg. Appl. 3(4), 3–29 (1999)

    MathSciNet  MATH  Google Scholar 

  7. Feng, Q.: Algorithms for drawing clustered graphs. Ph. D. thesis. The University of Newcastle, Australia (1997)

    Google Scholar 

  8. Feng, Q., Cohen, R.F., Eades, P.: How to Draw a Planar Clustered Graph. In: Li, M., Du, D.-Z. (eds.) COCOON 1995. LNCS, vol. 959, pp. 21–30. Springer, Heidelberg (1995)

    Chapter  Google Scholar 

  9. Feng, Q., Cohen, R.F., Eades, P.: Planarity for Clustered Graphs. In: Spirakis, P.G. (ed.) ESA 1995. LNCS, vol. 979, pp. 213–226. Springer, Heidelberg (1995)

    Chapter  Google Scholar 

  10. Jelínková, E., Kára, J., Kratochvíl, J., Pergel, M., Suchý, O., Vyskocil, T.: Clustered planarity: Small clusters in cycles and Eulerian graphs. J. Graph Alg. Appl. 13(3), 379–422 (2009)

    Article  MATH  Google Scholar 

  11. Jünger, M., Leipert, S., Percan, M.: Triangulating clustered graphs. Technical report. Zentrum für Angewandte Informatik Köln (2002)

    Google Scholar 

  12. Nagamochi, H., Kuroya, K.: Drawing c-planar biconnected clustered graphs. Discr. Appl. Math. 155(9), 1155–1174 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  13. Schaeffer, S.E.: Graph clustering. Computer Science Review 1(1), 27–64 (2007)

    Article  MathSciNet  Google Scholar 

  14. Tutte, W.T.: How to draw a graph. Proc. London Math. Soc. 13(52), 743–768 (1963)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

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

    Fabrizio Frati

Authors
  1. Fabrizio Frati
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Editor information

Editors and Affiliations

  1. School of IT, University of Sydney, Building J12, 2006, Sydney, NSW, Australia

    Joachim Gudmundsson , Julián Mestre  & Taso Viglas ,  & 

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Frati, F. (2012). Multilevel Drawings of Clustered Graphs. In: Gudmundsson, J., Mestre, J., Viglas, T. (eds) Computing and Combinatorics. COCOON 2012. Lecture Notes in Computer Science, vol 7434. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32241-9_27

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  • DOI: https://doi.org/10.1007/978-3-642-32241-9_27

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-32240-2

  • Online ISBN: 978-3-642-32241-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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