Polynomial kernels for Thinness under vertex cover or twin-cover

Ascertain whether the Thinness problem admits polynomial kernels when parameterized by the size of a minimum vertex cover or by the twin-cover number of the input graph.

Background

The paper gives FPT algorithms for Thinness under parameters related to modular partitions and obtains exponential kernels under vertex cover and twin-cover, but does not establish whether polynomial kernels are achievable.

They explicitly pose this as a kernelization question distinct from the algorithmic tractability results.

References

Possible avenues of research that this work leaves open include: Does Thinness admit polynomial kernels when parameterized by the vertex cover or the twin-cover number 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)