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International Workshop on Graph-Theoretic Concepts in Computer Science

WG 2003: Graph-Theoretic Concepts in Computer Science pp 168–179Cite as

Completely Connected Clustered Graphs

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2880))

Abstract

Planar drawings of clustered graphs are considered. We introduce the notion of completely connected clustered graphs, i.e. hierarchically clustered graphs that have the property that not only every cluster but also each complement of a cluster induces a connected subgraph. As a main result, we prove that a completely connected clustered graph is c-planar if and only if the underlying graph is planar. Further, we investigate the influence of the root of the inclusion tree to the choice of the outer face of the underlying graph and vice versa.

This work was partially supported by the DFG under grant BR 2158/1-1 and WA 654/13-1. It was also partially supported by the Human Potential Program of the EU under contract no HPRN-CT-1999-00104 (AMORE Project).

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References

  1. Bertault, F., Miller, M.: An algorithm for drawing compound graphs. In: Kratochvíl, J. (ed.) GD 1999. LNCS, vol. 1731, pp. 197–204. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  2. Brandes, U., Cornelsen, S., Wagner, D.: How to draw the minimum cuts of a planar graph. In: Marks, J. (ed.) GD 2000. LNCS, vol. 1984, pp. 103–114. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  3. Cornelsen, S.: Drawing Families of Cuts in a Graph. PhD thesis, Universität Konstanz (2003), http://www.ub.uni-konstanz.de/kops/volltexte/2003/975/

  4. Dahlhaus, E.: A linear time algorithm to recognize clustered planar graphs and its parallelization. In: Lucchesi, C.L., Moura, A.V. (eds.) LATIN 1998. LNCS, vol. 1380, pp. 239–248. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  5. Di Battista, G., Didimo, W., Marcandalli, A.: Planarization of clustered graphs. In: Mutzel, P., Jünger, M., Leipert, S. (eds.) GD 2001. LNCS, vol. 2265, pp. 60–74. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  6. Eades, P., Cohen, R.F., Feng, Q.: 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 

  7. Eades, P., Feng, Q.: Multilevel visualization of clustered graphs. In: North [18], pp. 101–112

    Google Scholar 

  8. Eades, P., Feng, Q., Lin, X.: Straight-line drawing algorithms for hierarchical graphs and clustered graphs. In: North [18], pp. 146–157

    Google Scholar 

  9. Eades, P., Feng, Q., Nagamochi, H.: Drawing clustered graphs on an orthogonal grid. Journal on Graph Algorithms and Applications 3(4), 3–29 (1999)

    MATH  MathSciNet  Google Scholar 

  10. Eades, P., Nagamochi, H., Feng, Q.: Straight-line drawing algorithms for hierarchical graphs and clustered graphs. Technical Report 98–03, Department of Computer Science and Software Engineering, University of Newcastle, Australia (1998), Available at ftp://ftp.cs.newcastle.edu.au/pub/techreports/tr98-03.ps.Z

  11. 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)

    Google Scholar 

  12. Goodrich, M.T., Kobourov, S.G. (eds.): GD 2002. LNCS, vol. 2528. Springer, Heidelberg (2002)

    MATH  Google Scholar 

  13. Gutwenger, C., Jünger, M., Leipert, S., Mutzel, P., Percan, M., Weiskircher, R.: Advances in c-planarity testing of clustered graphs. In: Goodrich and Kobourov [12], pp. 220–235

    Google Scholar 

  14. Huang, M.L., Eades, P.: A fully animated interactive system for clustering and navigating huge graphs. In: Whitesides, S.H. (ed.) GD 1998. LNCS, vol. 1547, pp. 374–383. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  15. Jünger, M., Leipert, S., Percan, M.: Triangulating clustered graphs. Technical Report zaik2002–444, Zentrum für Angewandte Informatik Köln (2002), Available at http://www.zaik.uni-koeln.de/%7Epaper/preprints.html?show=zaik2002-444

  16. Kant, G., Bodlaender, H.L.: Planar graph augmentation problems. In: Dehne, F., Sack, J.-R., Santoro, N. (eds.) WADS 1991. LNCS, vol. 519, pp. 286–298. Springer, Heidelberg (1991)

    Chapter  Google Scholar 

  17. Lütke-Hüttmann, D.: Knickminimales Zeichnen 4-planarer Clustergraphen. Master’s thesis, Universität des Saarlandes, Diplomarbeit (1999)

    Google Scholar 

  18. North, S.C. (ed.): GD 1996. LNCS, vol. 1190. Springer, Heidelberg (1997)

    MATH  Google Scholar 

  19. Raitner, M.: HGV: A library for hierarchies, graphs, and views. In: Goodrich and Kobourov [12], pp. 236–243

    Google Scholar 

  20. Sugiyama, K., Misue, K.: Visualization of structural information: Automativ drawing of compound digraphs. IEEE Transactions on Systems, Man and Cybernetics 21, 876–892 (1991)

    Article  MathSciNet  Google Scholar 

  21. Wang, X., Miyamoto, I.: Generating customized layouts. In: Brandenburg, F.J. (ed.) GD 1995. LNCS, vol. 1027, pp. 504–515. Springer, Heidelberg (1996)

    Chapter  Google Scholar 

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Author information

Authors and Affiliations

  1. Dipartimento di Ingegneria Elettrica, Università dell’Aquila,  

    Sabine Cornelsen

  2. Department of Computer Science, University of Karlsruhe,  

    Dorothea Wagner

Authors
  1. Sabine Cornelsen
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  2. Dorothea Wagner
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Editor information

Editors and Affiliations

  1. Department of Information and Computing Sciences, Utrecht University, The Netherlands

    Hans L. Bodlaender

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Cornelsen, S., Wagner, D. (2003). Completely Connected Clustered Graphs. In: Bodlaender, H.L. (eds) Graph-Theoretic Concepts in Computer Science. WG 2003. Lecture Notes in Computer Science, vol 2880. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39890-5_15

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  • DOI: https://doi.org/10.1007/978-3-540-39890-5_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-20452-7

  • Online ISBN: 978-3-540-39890-5

  • eBook Packages: Springer Book Archive

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