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Clustered Level Planarity

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SOFSEM 2004: Theory and Practice of Computer Science (SOFSEM 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2932))

Abstract

Planarity is an important concept in graph drawing. It is generally accepted that planar drawings are well understandable. Recently, several variations of planarity have been studied for advanced graph concepts such as k-level graphs [16, 15, 13, 14, 11, 12, 10, 6] and clustered graphs [7, 5]. In k-level graphs, the vertices are partitioned into k levels and the vertices of one level are drawn on a horizontal line. In clustered graphs, there is a recursive clustering of the vertices according to a given nesting relation. In this paper we combine the concepts of level planarity and clustering and introduce clustered k-level graphs. For connected clustered level graphs we show that clustered k-level planarity can be tested in \(\mathcal O(k|v|)\) time.

This research has been supported in part by the Deutsche Forschungsgemeinschaft, grant BR 835/9-1.

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Author information

Authors and Affiliations

  1. University of Passau, 94030, Passau, Germany

    Michael Forster & Christian Bachmaier

Authors
  1. Michael Forster
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  2. Christian Bachmaier
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Editor information

Editors and Affiliations

  1. Faculty of Sciences, ILLC - Department of Mathematics and Computer Science, University of Amsterdam, Plantage Muidergracht 24, 1018 TV, Amsterdam, The Netherlands

    Peter Van Emde Boas

  2. Faculty of Mathematics and Physics, Charles University, Prague

    Jaroslav Pokorný

  3. Institute of Informatics and Software Engineering Faculty of Informatics and Information technologies, Slovak University of Technology, Ilkovičova 3, 842 16, Bratislava

    Mária Bieliková

  4. Institute of Computer Science, Academy of Sciences of the Czech Republic, Pod Vodárenskou věží 2, 182 07, Prague 8 Czech Republic

    Július Štuller

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Forster, M., Bachmaier, C. (2004). Clustered Level Planarity. In: Van Emde Boas, P., Pokorný, J., Bieliková, M., Štuller, J. (eds) SOFSEM 2004: Theory and Practice of Computer Science. SOFSEM 2004. Lecture Notes in Computer Science, vol 2932. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24618-3_18

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  • DOI: https://doi.org/10.1007/978-3-540-24618-3_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-20779-5

  • Online ISBN: 978-3-540-24618-3

  • eBook Packages: Springer Book Archive

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