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 2 klog k on the number of obstructions, signi cantly improving the previously best-known bound of 2 pk. Our techniques have the added advantage of being considerably simpler than those of previous authors.
Arvind Gupta, Damon Kaller, Thomas C. Shermer