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Tree-Partitions of k-Trees with Applications in Graph Layout

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Graph-Theoretic Concepts in Computer Science (WG 2003)

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

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Abstract

A tree-partition of a graph is a partition of its vertices into ‘bags’ such that contracting each bag into a single vertex gives a forest. It is proved that every k-tree has a tree-partition such that each bag induces a (k-1)-tree, amongst other properties. Applications of this result to two well-studied models of graph layout are presented. First it is proved that graphs of bounded tree-width have bounded queue-number, thus resolving an open problem due to Ganley and Heath [2001] and disproving a conjecture of Pemmaraju [1992]. This result provides renewed hope for the positive resolution of a number of open problems regarding queue layouts. In a related result, it is proved that graphs of bounded tree-width have three-dimensional straight-line grid drawings with linear volume, which represents the largest known class of graphs with such drawings.

Research supported by NSERC and FCAR.

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Author information

Authors and Affiliations

  1. School of Computer Science, McGill University, Montréal, Canada

    Vida Dujmović

  2. School of Computer Science, Carleton University, Ottawa, Canada

    David R. Wood

Authors
  1. Vida Dujmović
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  2. David R. Wood
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Editors and Affiliations

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

    Hans L. Bodlaender

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Dujmović, V., Wood, D.R. (2003). Tree-Partitions of k-Trees with Applications in Graph Layout. 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_18

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  • DOI: https://doi.org/10.1007/978-3-540-39890-5_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-20452-7

  • Online ISBN: 978-3-540-39890-5

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