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 \(H \in \mathcal{G}\) with the property 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 \(\mathfrak{T}\mspace{-1.5mu}\mathfrak{P}\) of trivially-perfect graphs we show that \(\mathfrak{T}\mspace{-1.5mu}\mathfrak{P}\)-width is NP-complete and we present fixed-parameter algorithms.
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Hung, LJ., Kloks, T., Lee, C.M. (2009). Trivially-Perfect Width. In: Fiala, J., Kratochvíl, J., Miller, M. (eds) Combinatorial Algorithms. IWOCA 2009. Lecture Notes in Computer Science, vol 5874. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10217-2_30
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DOI: https://doi.org/10.1007/978-3-642-10217-2_30
Publisher Name: Springer, Berlin, Heidelberg
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