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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Hung, LJ., Kloks, T. (2010). On Some Simple Widths. In: Rahman, M.S., Fujita, S. (eds) WALCOM: Algorithms and Computation. WALCOM 2010. Lecture Notes in Computer Science, vol 5942. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11440-3_19
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DOI: https://doi.org/10.1007/978-3-642-11440-3_19
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