Abstract
We introduce new techniques for studying the structure of partial k-trees. In particular, we show that the complements of partial k-trees provide an intuitively-appealing characterization of partial k-tree obstructions. We use this characterization to obtain a lower bound of 2Ω(k log k) on the number of obstructions, significantly improving the previously best-known bound of \(2^{\Omega \left( {\sqrt k } \right)} \). Our techniques have the added advantage of being considerably simpler than those of previous authors.
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© 1999 Springer-Verlag Berlin Heidelberg
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Gupta, A., Kaller, D., Shermer, T. (1999). On the Complements of Partial k-Trees. In: Wiedermann, J., van Emde Boas, P., Nielsen, M. (eds) Automata, Languages and Programming. Lecture Notes in Computer Science, vol 1644. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48523-6_35
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DOI: https://doi.org/10.1007/3-540-48523-6_35
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