FPT computation of Kelly-width

Determine whether computing the Kelly-width of a digraph admits a fixed-parameter tractable algorithm.

Background

The paper relates Kelly-width to the strong directed coloring number and places it within a hierarchy of digraph width parameters. It records an unresolved algorithmic question previously posed in the literature concerning fixed-parameter computation of Kelly-width.

References

Meister, Telle, and Vatshelle asked whether there exists an FPT algorithm for computing Kelly-width. This remains an open problem.

— Unavoidable butterfly minors in digraphs of large cycle rank  (2507.11814 - Hatzel et al., 16 Jul 2025) in Section Conclusion