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Directed Rank-Width and Displit Decomposition

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Graph-Theoretic Concepts in Computer Science (WG 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5911))

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Abstract

Rank-width is a graph complexity measure that has many structural properties. It is known that the rank-width of an undirected graph is the maximum over all induced prime graphs with respect to split decomposition and an undirected graph has rank-width at most 1 if and only if it is a distance-hereditary graph. We are interested in an extension of these results to directed graphs. We give several characterizations of directed graphs of rank-width 1 and we prove that the rank-width of a directed graph is the maximum over all induced prime graphs with respect to displit decomposition, a new decomposition on directed graphs.

Research supported by the French ANR-project ”Graph decompositions and algorithms” (GRAAL).

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Author information

Authors and Affiliations

  1. LIMOS - Université Blaise Pascal, France

    Mamadou Moustapha Kanté

  2. LABRI - Université Bordeaux 1, France

    Michaël Rao

Authors
  1. Mamadou Moustapha Kanté
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  2. Michaël Rao
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Editor information

Editors and Affiliations

  1. CNRS - LIRMM, 161 rue Ada, 34392, Montpellier Cedex 5, France

    Christophe Paul

  2. LIAFA, case 7014, Université Paris Diderot, 75205, Paris Cedex 13, France

    Michel Habib

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Kanté, M.M., Rao, M. (2010). Directed Rank-Width and Displit Decomposition. In: Paul, C., Habib, M. (eds) Graph-Theoretic Concepts in Computer Science. WG 2009. Lecture Notes in Computer Science, vol 5911. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11409-0_19

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  • DOI: https://doi.org/10.1007/978-3-642-11409-0_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-11408-3

  • Online ISBN: 978-3-642-11409-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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