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International Computing and Combinatorics Conference

COCOON 2018: Computing and Combinatorics pp 255–267Cite as

Directed Path-Width and Directed Tree-Width of Directed Co-graphs

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10976))

Abstract

In this paper we consider the directed path-width and directed tree-width of directed co-graphs. As an important combinatorial tool, we show how the directed path-width and the directed tree-width can be computed for the disjoint union, series composition, and order composition of two directed graphs. These results imply the equality of directed path-width and directed tree-width for directed co-graphs and a linear-time solution for computing the directed path-width and directed tree-width of directed co-graphs, which generalizes the known results for undirected co-graphs of Bodlaender and Möhring.

C. Rehs—The work of the second author was supported by the German Research Association (DFG) grant GU 970/7-1.

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Notes

  1. 1.

    The proofs of the results marked with a are omitted due to space restrictions.

  2. 2.

    Please note that our definition of Z-normality differs slightly from the definition in [16] but this trivially makes no difference for the directed tree-width.

  3. 3.

    A remarkable difference to the undirected tree-width [20] is that the sets \(W_r\) have to be disjoint and non-empty.

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Authors and Affiliations

  1. Algorithmics for Hard Problems Group, Institute of Computer Science, Heinrich-Heine-University Düsseldorf, 40225, Düsseldorf, Germany

    Frank Gurski & Carolin Rehs

Authors
  1. Frank Gurski
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  2. Carolin Rehs
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Correspondence to Carolin Rehs .

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Editors and Affiliations

  1. City University of Hong Kong, Hong Kong, China

    Lusheng Wang

  2. Shandong University, Jinan, China

    Daming Zhu

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Gurski, F., Rehs, C. (2018). Directed Path-Width and Directed Tree-Width of Directed Co-graphs. In: Wang, L., Zhu, D. (eds) Computing and Combinatorics. COCOON 2018. Lecture Notes in Computer Science(), vol 10976. Springer, Cham. https://doi.org/10.1007/978-3-319-94776-1_22

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  • DOI: https://doi.org/10.1007/978-3-319-94776-1_22

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  • Print ISBN: 978-3-319-94775-4

  • Online ISBN: 978-3-319-94776-1

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