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 \(\mathbb{N}_1,\dots,\mathbb{N}_{\rm \tt k}\) in G such that G can be embedded into a graph \({\rm H \in \mathcal{G}}\) 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 ℕi. For the class \(\mathfrak{B}\) of block graphs we show that \(\mathfrak{B}\)-width is NP-complete and we present fixed-parameter algorithms.
This research is supported by the National Science Council of Taiwan under grant NSC97–2221–E–194–055.
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Chang, MS., Hung, LJ., Kloks, T., Peng, SL. (2009). Block-Graph Width. In: Chen, J., Cooper, S.B. (eds) Theory and Applications of Models of Computation. TAMC 2009. Lecture Notes in Computer Science, vol 5532. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02017-9_18
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DOI: https://doi.org/10.1007/978-3-642-02017-9_18
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-02016-2
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