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\(\mathbb F\)-Rank-Width of (Edge-Colored) Graphs

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Algebraic Informatics (CAI 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6742))

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Abstract

Rank-width is a complexity measure equivalent to the clique-width of undirected graphs and has good algorithmic and structural properties. It is in particular related to the vertex-minor relation. We discuss an extension of the notion of rank-width to all types of graphs - directed or not, with edge colors or not -, named \(\mathbb F\)-rank-width. We extend most of the results known for the rank-width of undirected graphs to the \(\mathbb F\)-rank-width of graphs: cubic-time recognition algorithm, characterisation by excluded configurations under vertex-minor and pivot-minor, and algebraic characterisation by graph operations. We also show that the rank-width of undirected graphs is a special case of \(\mathbb F\)-rank-width.

A part of this research is supported by the projects “Graph decompositions and algorithms (GRAAL)” and “Decomposition Of Relational Structures and Combinatorial Optimisation (DORSO)” of French “Agence Nationale Pour la Recherche” and was done when the first author was in Université Bordeaux 1, LaBRI.

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Author information

Authors and Affiliations

  1. Clermont-Université, Université Blaise Pascal, LIMOS, CNRS, France

    Mamadou Moustapha Kanté

  2. CNRS - Laboratoire J.V. Poncelet, Moscow, Russia

    Michael Rao

  3. Université de Bordeaux, LaBRI, CNRS, France

    Michael Rao

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

Editors and Affiliations

  1. Research Institute for Symbolic Computation (RISC), Johannes Kepler University, Altenberger Straße 69, 4040, Linz, Austria

    Franz Winkler

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Kanté, M.M., Rao, M. (2011). \(\mathbb F\)-Rank-Width of (Edge-Colored) Graphs. In: Winkler, F. (eds) Algebraic Informatics. CAI 2011. Lecture Notes in Computer Science, vol 6742. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21493-6_10

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  • DOI: https://doi.org/10.1007/978-3-642-21493-6_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-21492-9

  • Online ISBN: 978-3-642-21493-6

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