Find coarse characterizations of k-path-breadth

Investigate whether generalizations of the graph parameters considered in the paper coarsely describe the k-path-breadth of a graph.

Background

The paper defines k-path-breadth by allowing each bag of a path-decomposition to be covered by at most k graph disks of a common radius. The authors explain that this generalizes ordinary path-breadth, which corresponds to k=1, and ask whether the structural parameters developed in the paper have analogous coarse-equivalence relationships for this broader notion.

References

It would be interesting to investigate if there exist generalizations of some graph parameters considered in this paper that coarsely describe the $k$-path-breadth.

— Graph parameters that are coarsely equivalent to path-length  (2503.05661 - Dragan et al., 7 Mar 2025) in Section 5, “Concluding remarks and open questions,” immediately after the definition of k-path-breadth