On the Complements of Partial k-Trees

Authors:
Arvind Gupta;Damon Kaller;Thomas C. Shermer
Affiliations:
-;-;-
Venue:
ICAL '99 Proceedings of the 26th International Colloquium on Automata, Languages and Programming
Year:
1999

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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 2Ω(√k). Our techniques have the added advantage of being considerably simpler than those of previous authors.