Recognition of Bounded Continuous Treewidth

Determine whether recognizing whether the one-bramble number of a continuous graph is at most a given integer k is tractable, particularly for small fixed k.

Background

The paper defines continuous treewidth as the one-bramble number, extending the classical bramble characterization of treewidth. It observes that recognizing whether this parameter is at most k may be substantially more difficult than the corresponding classical problem and explicitly leaves its tractability unresolved.