Bounded DAG-width versus bounded Kelly-width

Determine whether every class of digraphs with bounded DAG-width also has bounded Kelly-width.

Background

The paper presents a hierarchy connecting directed width parameters and coloring numbers. In that hierarchy, the implication from bounded DAG-width to bounded Kelly-width is explicitly marked as unresolved.

References

Whether or not every class of bounded DAG-width has bounded Kelly-width is an open problem.

— Unavoidable butterfly minors in digraphs of large cycle rank  (2507.11814 - Hatzel et al., 16 Jul 2025) in Figure 1 caption, Figure labeled “The hierarchy of the mentioned digraph classes”