Optimality of the 2^{O(k log k)} running times

Determine whether the 2^{O(k log k)} 3 n running times obtained for the other vertex-cover-parameterized algorithms in the paper are optimal.

Background

Several unweighted and pre-weighted variants are solved in time 2{O(k log k)} 3 n when parameterized by vertex cover number. The paper does not establish matching lower bounds or rule out substantially faster dependence on k.

The authors therefore leave open the question of whether these running-time bounds reflect an inherent complexity barrier or can be improved.

References

A related question is whether the other running times of 2{O(k \log k)} \cdot n can be shown to be optimal.

— Vertex-Coloring Edge-Weighting: Kernelization and Generalization  (2609.27719 - Aute et al., 23 Sep 2026) in Section 7, paragraph titled “Open problems”