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On the Tree-Degree of Graphs

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Graph-Theoretic Concepts in Computer Science (WG 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2204))

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Abstract

Every graph is the edge intersection graph of subtrees of a tree. The tree-degree of a graph is the minimum maximal degree of the underlying tree for which there exists a subtree intersection model. Computing the tree-degree is NP-complete even for planar graphs, but polynomial time algorithms exist for outer-planar graphs, diamond-free graphs and chordal graphs. The number of minimal separators of graphs with bounded tree-degree is polynomial. This implies that the treewidth of graphs with bounded tree-degree can be computed efficiently, even without the model given in advance.

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Author information

Authors and Affiliations

  1. Department of Computer Science and Information Engineering, Chung Cheng University, Ming-Shiun, Chiayi 621, Taiwan

    Maw-Shang Chang

  2. School of Computing, University of Leeds, Leeds, LS2 9JT, UK

    Haiko Müller

Authors
  1. Maw-Shang Chang
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  2. Haiko Müller
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Rostock, 18051, Rostock, Germany

    Andreas Brandstädt  & Van Bang Le  & 

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© 2001 Springer-Verlag Berlin Heidelberg

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Chang, MS., Müller, H. (2001). On the Tree-Degree of Graphs. In: Brandstädt, A., Le, V.B. (eds) Graph-Theoretic Concepts in Computer Science. WG 2001. Lecture Notes in Computer Science, vol 2204. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45477-2_6

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  • DOI: https://doi.org/10.1007/3-540-45477-2_6

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42707-0

  • Online ISBN: 978-3-540-45477-9

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