Thinness parameterized by treewidth

Investigate whether the Thinness problem is fixed-parameter tractable or slice-wise polynomial when parameterized by the treewidth of the input graph.

Background

Beyond parameterization by solution size, the paper explores relationships between thinness and several graph width parameters, proving kernelization lower bounds for some but not resolving algorithmic tractability for thinness under treewidth.

The authors emphasize that the ordering aspect in thinness complicates the application of logic-based meta-theorems to obtain FPT results under treewidth.

References

Possible avenues of research that this work leaves open include: Is Thinness FPT (or even XP) when parameterized by other parameters, like for example the treewidth of the input graph?

— Computing parameters that generalize interval graphs using restricted modular partitions (2512.22975 - Bonomo-Braberman et al., 28 Dec 2025) in Section 9 (Conclusions and open problems)