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On Some Simple Widths

  • Ling-Ju Hung
  • Ton Kloks
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5942)

Abstract

The \(\mathcal{G}\)-width of a class of graphs \(\mathcal{G}\) is defined as follows. A graph G has \(\mathcal{G}\)-width k if there are k independent sets ℕ1,...,ℕ k in G such that G can be embedded into a graph \(H \in \mathcal{G}\) such that for every edge e in H which is not an edge in G, there exists an i such that both endpoints of e are in ℕ i . For the class \(\mathfrak{C}\) of cographs we show that \(\mathfrak{C}\)-width is NP-complete. We show that the recognition is fixed-parameter tractable, and we show that there exists a finite obstruction set. We introduce simple-width as an alternative for rankwidth and we characterize the graphs with simple-width at most two.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Ling-Ju Hung
    • 1
  • Ton Kloks
    • 1
  1. 1.Department of Computer Science and Information EngineeringNational Chung Cheng UniversityTaiwan

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